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Page 1 of 57
Illumination Simulation and Design Considerations for Mobile Virtual Reality
Systems Evan Richards
Opti 909 – Report for Masters of Science in Optical Sciences
November 16, 2015
Introduction
Head mounted displays (HMDs) have been in wide military and commercial use for decades [1].
HMDs present visual information to the user, whether it be symbols, text, or imagery. These
devices come in a variety of design forms and can be transparent or occluded [2] [3]. Within the
past four years, consumer electronics versions of HMDs have been front page news through
developer kits like Google Glass Explorer Edition and the pending launch of the consumer
Oculus Rift in the first quarter of 2016.
In general, consumer HMDs fall into three classes of development – informative/microinteration,
augmented reality, and virtual reality. Some classify the informative/microinteraction devices as
smart glasses or smart eyewear [4]. This first category includes Google Glass [5], seen in Figure
1, where the HMD may sit above the eye and outside of the straight ahead gaze of the user.
These systems tend to have small diagonal fields of view, less than 20 degrees, in order to
optimize for compactness and minimum visibility for those around the user. In an effort to
enhance usability beyond information display, these systems may include cameras, audio, and
other input interaction. Many times these optics can be see through, as is the case with Google
Glass incorporating a partially transparent beamsplitter and large fully transparent section of the
light pipe. This allows the user to still directly see the physical environment when looking
through the device. Due to the field of view and the placement out of the straight forward gaze
position, these devices do not overlay information directly on top of the environment and are not
considered augmented reality. As these are intended for everyday use, minimizing weight and
size are critical considerations and highly constrain the optical system. This is one of the reasons
that Google Glass used a single spherical mirror to act as a magnifier and not form a pupil for the
user.
Figure 1. Google Glass sitting above the user’s eye [6].
Page 2 of 57
Augmented reality (AR) systems intend to overlay content on top of the real world in real time
[7]. In this case, the optics are placed directly in front of the user’s forward gaze. These systems
require larger fields of view than the smart glasses category. Combined with the requirement for
see through performance, these systems require more complex optics for enhanced performance.
As an example of complexity, the DK40 [8], a development kit made by Lumus Ltd., uses a
collimator combined with a lightguide containing a series of parallel beamsplitters to present the
image to the user. This model offers 25 degrees FFOV, while other models offer up to 40
degrees FFOV. Illustrations of the technology are shown in Figure 2.
a) b) Figure 2. Lumus DK40 lightguide for AR [8].
Microsoft recently announced developer kits for the HoloLens system, but a minimal amount of
public information is known about the optical architecture of the system [9]. Figure 3 shows the
graphics on Microsoft’s HoloLens website, noting the use of holographic optics to create AR.
Holographic combiners can be thin as shown in the figure, but tend to have narrow FOV. This
narrow FOV is challenging for the AR space.
Figure 3. Hardware information available from Microsoft HoloLens website [9].
Freeform optics are showing great promise in this area by eliminating some of the issues that
conventional systems have scaling to larger fields of view. Additionally, demonstrations of
hardware have been performed that present integral imaging and freeform optics to provide relief
to eye fatigue, such as the optical layout shown in Figure 4 [7]. The optics enable compact
Page 3 of 57
designs along with several depth planes to eliminate conflicting depth perception. With a
freeform optic providing the projection, a secondary freeform corrector lens is added to the
system to prevent distortion of the see through image. In addition to multiple depth planes,
compact eye tracking has been demonstrated for AR freeform systems by placing an IR camera
near the microdisplay [10]. Even with freeforms, AR systems can still be bulky and very
apparent when on the face of the user.
Figure 4. AR freeform system consisting of freeform combiner and freeform see through corrector.
This system also generates several depth planes [7].
In contrast to AR systems, virtual reality (VR) systems intend to fully replace the physical world.
As such, the optical designs incorporate fully occluded optics and allow a variety of design
options for screen size and optical complexity. These systems have large fields of view greater
than 90 degrees full field of view (FFOV) in order to immerse the user and provide a sense of
VR presence. The size of the system enables the use of much larger (diameter and thickness)
optics to create the wide field of view. Some of these systems, such as the Oculus Rift DK2, use
rotationally symmetric systems with one single lens placed in front of each eye to magnify the
display in a non-pupil forming architecture. Systems like Oculus Rift make use of powerful
desktop PCs to render a large number of pixels at high frame rates. This requires the user to be
relatively stationary or within a bounded environment. Thus, occluded displays can be used and
are desired to also block out the external environment.
Mobile phones and AMOLED displays have now reached the performance level where they are
capable of rendering VR experiences. In 2014, Oculus VR and Samsung Electronics announced
the Gear VR Innovator Edition mobile virtual reality headset [11]. The system consists of two
separate parts – a Galaxy Note 4 cell phone and a headset rig. The phone is installed into the
headset rig and locks into place relative to magnifying optics. Mechanical features locate the
display inside the front focal point of the lens to create an enlarged, virtual image in front of the
user. This is a non-pupil forming architecture. Views of the system with and without the Note 4
installed, along with the user’s view of the optics, are shown in Figure 5. Since that time, a new
Page 4 of 57
innovator edition has been released for the Galaxy S6 smartphone and has been additionally
buoyed by the announcement of a $99 version of Gear VR [12].
a) b)
c)
Figure 5. a) Separated Gear VR and Note 4. b) Note 4 installed into Gear VR harness. c) View of
system while on from the user side [13].
Table 1 lists the requirements for different classifications of HMDs. The authors of the
comparison do not explicitly call out the requirements from AR. In this regard, many of the
requirements for smart glasses can be applied to AR headsets, but with larger field of view and
proper registration to overlay content on the real world. VR headsets also require spatial and
inertial tracking that smart glasses do not require.
Page 5 of 57
Table 1. Comparison of requirements for various HMDs [4].
Illumination Considerations for Consumer HMDs
As with many other systems, it is important to evaluate the complete performance before
entering production. Non-sequential ray tracing models allow the analysis to include multiple
interactions between the optical and mechanical elements that are not captured in sequential ray
tracing models like Zemax or Code V. Material properties, such as coatings and absorption, can
be easily included and analyzed. The flexibility to define the illumination source size, location,
spectral content and spatial and angular distributions provide the essentials for defining the
requirements of the display or analyzing candidate technology.
The three classes of devices each have their own unique challenges that require analysis using a
non-sequential model. The first case is to analyze the illumination path exclusively, with the
source, optics and mechanics being the surfaces analyzed. Using Google Glass as an example
for the microinteraction category, the compact size of the beamsplitter creates the risk of
reflections of the primary image. If the top and bottom surfaces of the beamsplitter are specular
or nearly specular, a case may occur as seen in Figure 6. Some of these reflections can be seen
on the Google Glass Explorer Edition. Similar cases may occur for AR systems as well as
compact performance is desired. Holographic and diffractive systems have the risk of multiple
images or crosstalk between spectral channels. This can result in overlapping images seen once
performing analysis with the complete system and its complete spectral parameters. For VR
systems, the primary concern is eliminating distractions presented to the user. Since the Gear
VR uses rotationally symmetric optics, the main concern is stray or scattered light from the
optics and housing.
Page 6 of 57
a) b) Figure 6. a) Desired image and b) example parasitic reflections from the surfaces of the
beamsplitter in Google Glass. Images adapted from [14].
The second case is to evaluate the impact of light from the environment to the user. For the
cases of microinteraction and AR devices, the environment plays a very strong role. These
devices have the goal of showing information out in the world, either informatively or overlayed
upon the environment. Optics with planar surfaces, such as Google Glass or the visor from
HoloLens, can reflect sunlight or other bright light sources to the user. These appear like glare
from the road when driving, or reflections from the surface of a lake. Making an illumination
model with external sources is the way to analyze this case. In VR systems, the concern is any
light leakage from the outside environment to the user. This can come from gaps or holes
between the system and the user’s face or gaps that occur between the cellphone and the headset
for the case of Gear VR. This could be done using an external source, like a lamp or the sun, and
CAD models of a user’s head with the Gear VR in compression against the CAD head.
For this report, the illumination path from display to the user’s eye will be evaluated for the Gear
VR system. Since no design files are available for the Gear VR, this model will be created
entirely based on measurements of a purchased Gear VR headset and Note 4 phone. Some of
these measurements may not be exact, such as physical dimensions measured with calipers rather
than a coordinate measuring machine (CMM). Reasonable assumptions and design methods will
be used along the way to create the final model. The case of stray light from the environment
will not be addressed in this report.
The objectives of this report are as follows: 1) perform on- and off-axis measurements to model
the Note 4 display, 2) create a viewing lens design based on measurements and specifications of
the Gear VR headset, 3) create a reasonable solid model of the opto-mechanical mounting of the
Gear VR, 4) import all geometry into LightTools for the illumination model and 5) verify
performance of the initial model, 6) update the eye model used as a receiver for both narrow and
wide FOV assessment, and 7) perform a stray light analysis of the system.
Page 7 of 57
Note 4 Measurements
The source is arguably the most critical part of an illumination model to set up. In the case of
LCD systems, a fully defined model will typically include a reflector, textured backlight, optical
source (like LEDs), diffusers, brightness enhancing films, liquid crystal performance, and
polarizers [15]. An example is shown in Figure 7.
Figure 7. Typical LCD and backlight structure [15].
If the 3D geometry and materials of these items are not available, one can collect or specify
performance for the flux, distribution, viewing angle and spectral/color content. This is the case
used in this analysis for the AMOLED display used in Gear VR. When looking at cell phone
displays like the Note 4, information is not typically provided by manufactures aside from basic
information. All display information from the Samsung Note 4 website is provided in Table 2.
The information from Samsung was useful to create the size of the display in the illumination
model.
Table 2. Key display parameters as listed on Samsung Galaxy Note 4 website [16].
Item Specification
Display type Quad HD Super AMOLED
Display resolution (HxV, pixels) 2560x1440
Display diagonal (mm) 143.9
Display pixel pitch (mm, calculated) 0.049
Phone dimensions (WxLxH, mm) 153.5x78.6x8.5
Gathering the spectral content from the display is a basic requirement for the illumination model.
With the AMOLED display, three spectral peaks are expected and those peaks can be used as the
primary wavelengths for the viewing optics design. Since this isn’t readily provided by
Samsung, measurements of a samples Note 4 display can be made to determine this information.
A spectroradiometer, such as those made by Photo Research Inc. or Konica Minolta, will
measure luminance, spectral radiance, and chromaticity over a small cone angle of <2 degrees
[17] [18]. These measurements were taken in the lab with a Photo Research PR-745
Page 8 of 57
spectroradiometer. The instrument had been calibrated within the past year at the Photo
Research headquarters.
For measurement setup, the Note 4 was oriented vertically using adhesive to mount the Note 4 to
a pair of optical posts on a rotation stage. The PR-745 was oriented such that its optical axis was
horizontal and normal to the display surface using the mounting features of the optical table. For
each measurement, the display was rotated to the desired measurement angle. The aim spot was
checked in the visual viewfinder of the PR-745 to ensure that the measurement was spatially
centered on the center of the display and that no clipping occurred on the sides of the display.
Figure 8. Setup for measuring Note 4 display performance over viewing angle. Display emitting
surface centered over rotation stage axis. Viewed from top down.
The Note 4 has several modes of operation that change the performance of the screen [19]. To
be consistent throughout the testing, the display was set to maximum brightness with the
adjustment for ambient light turned off. Basic Mode (sRGB/Rec. 709) was selected for the color
space although the color space used on the Note 4 during VR operation is not known. Images for
testing were created in Adobe Photoshop and saved as BMPs with no color management.
Images were displayed on the device using the default Google Photos app after being transferred
via USB. The parameters and results of the on-axis measurement at the center of the screen are
summarized in Table 3. Chromaticity values are reported using CIE 1931 2 degree observer.
Measured spectral radiance is shown in Figure 9.
Page 9 of 57
Table 3. On-axis measurement parameters and results for the Note 4 display. All values collected
via laboratory measurement.
Item Specification/Result
Instrument Photo Research PR-745 with MS-75 lens
Measurement aperture (degrees) 2
Measurement bandwidth (nm) 4
Instrument to display distance (m) 0.57
Display operation mode Basic Mode
Display system settings Full brightness, ambient light sensor off
White image brightness (nits) 330.1
Red image brightness (nits) 70.82
Green image brightness (nits) 232.6
Blue image brightness (nits) 20.45
White color coordinate (x, y) (0.3100, 0.3271)
Red color coordinate (x, y) (0.6370, 0.3344)
Green color coordinate (x, y) (0.2856, 0.6060)
Blue color coordinate (x, y) (0.1541, 0.0537)
White image CCT (K) 6457
Figure 9. Plot of on-axis spectral radiance for white, red, green and blue primary images.
In order to determine if the display was Lambertian as assumed, the measurements were taken at
various angles relative to the display surface normal. Equations for luminance are shown in Eqs.
(1) and (2).
𝐿𝑣 =𝑑2Φ𝑣
𝑑𝐴𝑠,𝑝𝑟𝑜𝑗𝑑Ω (1)
𝐿(𝑟, 𝜃, 𝜙) = 𝐿(𝑟) = 𝐿𝑠 (2)
0.00E+00
2.00E-03
4.00E-03
6.00E-03
8.00E-03
1.00E-02
1.20E-02
1.40E-02
38
0
40
0
42
0
44
0
46
0
48
0
50
0
52
0
54
0
56
0
58
0
60
0
62
0
64
0
66
0
68
0
70
0
72
0
74
0
76
0
78
0
W/s
r/m
^2/n
m
Wavelength (nm)
Note 4 Spectral Radiance
White
Red
Green
Blue
Page 10 of 57
Equation 2 assumes that the source has uniform spatial emission. The spectroradiometer
measures a fixed angle and is focused at a single distance. The measured result will be an
average over the spatial measurement area. This means that dAs,proj and dΩ are constant for the
spectroradiometer measurements. Thus, if the source is Lambertian, all luminance
measurements will be the same regardless of angle. The Note 4 display was measured using the
same conditions listed above from 0 to 60 degrees AOI relative to the surface normal, in steps of
5 degrees, using a white image. The luminance measurements are shown in Figure 10.
Figure 10. Plot of luminance over angle measurements for Note 4.
The display does not exhibit Lambertian behavior beyond 10 degrees to the surface normal. This
may be caused by the performance of the circular polarizer on top of the display. It is
worthwhile to also look at the spectral content variation over angle. Some minor color variations
were noted and were seen in the data as well. Because of the close spacing of some of the
curves, these plots are shown in Figure 11 in intervals of 10 degrees. Because of the
performance and the interest in looking at color over viewing angle, this will need to be
addressed in the LightTools model.
0
50
100
150
200
250
300
350
0 10 20 30 40 50 60
Lum
inan
ce (
nit
s)
Angle from Normal (deg)
Note 4 Luminance over Angle
Page 11 of 57
Figure 11. Spectral Radiance of Note 4 display as measured over angle. AOI denotes the angle
relative to the display normal. Rotations were performed in the horizontal axis.
It is advantageous to include this information on a spectral basis into LightTools. Rays are
generated within the specified wavelength region for the source and the proper power applied
based on the particular wavelength of the ray. For comparison purposes, it is easier to see the
white point plotted in different forms. First, Figure 12 shows the color difference at various
vireing angles relative to the viewing the display at the surface normal. Second, Figure 13 shows
the plot of these white points overlaid on the CIE 1931 and CIE 1976 color diagrams.
Perceptually, a small color shift can be observed when looking at higher angles relative to the
display normal even though the grouping on the color space diagrams appears tight. This will be
an item to watch through later analysis.
Figure 12. Color difference in CIE 1976 from on-axis measurement for Note 4 display.
0.00E+00
2.00E-03
4.00E-03
6.00E-03
8.00E-03
1.00E-02
1.20E-02
1.40E-02
1.60E-02
38
04
00
42
04
40
46
04
80
50
05
20
54
05
60
58
06
00
62
06
40
66
06
80
70
07
20
74
07
60
78
0
W/s
r/m
^2/n
m
Wavelength (nm)
Note 4 Spectral Radiance over Angle
0° AOI
10° AOI
20° AOI
30° AOI
40° AOI
50° AOI
60° AOI
0.000
0.005
0.010
0.015
0.020
0.025
0 10 20 30 40 50 60
Δu
'v'
Angle from Normal (degrees)
Note 4 Δu'v' from On-Axis Measurement
Page 12 of 57
a) b) Figure 13. Scatter distribution of the white point by viewing angle for Note 4 display in a) CIE
1931 and b) CIE 1976 color spaces. Data labels not included due to tight grouping. CIE images
adapted from [20] and [21].
Viewing Lens Design
As previously noted, the lens prescription for the Gear VR headset rig is not available.
Inspection shows that the system uses a single lens with no coatings on the lens surfaces. The
starting point for the design comes from the Samsung Gear VR website and are listed in Table 4.
The interpupillary distance for the headset is adjustable using a knob on the headset. For ease of
nomenclature, surface 1 will designate the lens surface closest to the user’s eye and surface 2
will designate the lens surface closest to the display
Table 4. Key system parameters as listed on Samsung Gear VR website [22].
Item Specification
Full field of view (per eye, degrees) 96
Focal adjustment Included
Interpupillary Distance (IPD) setting (mm) 55-71
Headset dimensions (WxLxH, mm) 198x116x90
Since the physical parts are available for inspection, a number of parameters were measured
from the Gear VR hardware. For the lens itself, the clear aperture was directly measured at
36mm. Using a series of measurements on the housing to the lens vertices, the lens thickness
was determined to be 12mm with a distance from the last surface to the screen of 26mm. Using
the thickness of the lens retainer, the sag on surface 1 was constrained to be less than 5.5mm.
This sag requirement is important to not have a highly protruding lens surface towards the user’s
eye.
Page 13 of 57
The lens was entered into Zemax, tracing from the stop to the display, and made into a rough
spherical version of the lens as a starting point. The object was placed at infinity. The eye relief,
which was initially set to 15mm, was reduced to 10mm for vignetting reasons. For material
selection, a low cost polymer option was selected. Two designs were run in parallel – one with
polycarbonate and one with PMMA. At first, the higher index of the polycarbonate was
appealing (1.5855 vs. 1.4918), but the PMMA was selected for its higher Abbe number when
considering polychromatic performance (57.441 vs. 29.909). From a manufacturing perspective,
PMMA also produces less wear on the injection molding tool. Finally, the design wavelengths
were selected based on the measured peak wavelengths for the red, green and blue output of the
AMOLED display.
Since the system is tracing from the stop to the display, the complete system appears like a
conventional landscape lens. Setting an appropriate stop size is important to understand the
magnitude of aberrations that the user will encounter in typical use. This value can be
determined based on experimental results that measured eye pupil diameter based on ambient
brightness. Figure 14 shows two studies measuring pupil diameter for extended illumination in
young eyes and narrow 10 degree illumination [23]. With the Note 4 display measuring at 330
nits, a reasonable selection of pupil size for this display is 4-6mm. The lens was optimized at
5mm stop diameter, and then stopped down to 4mm to reduce the vignetting at the largest field
angle.
Figure 14. Plot of human pupil diameter as a function of illumination. Extended illumination is
shown with the blue line, and 10 degree illumination is shown with the red line [23].
Field points were added in Zemax to sample every 5 degrees from 0 to 45 degrees and a final
field at 48 degrees was added. A default merit function to optimize for RMS spot size (x + y
instead of radius) relative to the centroid was included with the sag requirement for surface 1.
All field points were given equal weights in the merit function. This was due to the lack of eye
tracking and thus the eye can look at any point in the field and not just the central foveal region.
Page 14 of 57
The system was iteratively optimized. The first optimization allowed the radii of curvature to
vary, with the resulting lens showing very strong field curvature. The second optimization
allowed the radii of curvature to vary along with the conic for surface 2. This result improved
the field curvature substantially. Finally, the radii of curvature and conics for both surface 1 and
surface 2 were allowed to vary. The key parameters and results are listed in Table 5. The optical
prescription is listed in Table 6.
Table 5. Key system parameters, specifications and results for the viewing lens design.
Item Specification Result
Virtual image distance (m) Infinity Same
Full field of view (degrees) 96 Same
Measured clear aperture (mm) 36 Same
Measured lens thickness (mm) 12 Same
Measured lens to screen distance (mm) 26 Same
Eye relief (mm) 15 10
Pupil diameter (mm) 5 4
Lens material PMMA or Polycarbonate PMMA
Eye side lens surface sag (mm) <5.5 4.261
Edge thickness (mm) >0 2.083
Design wavelengths (nm) 458, 530, 612 Same
Table 6. Optical prescription for viewing lens. All units in mm.
Surface Radius Thickness Material Semi Diameter Conic
0 - Object Infinity Infinity Infinity
1 - Stop (Eye Relief) Infinity 10.000 2.000
2 - Lens 35.424 12.000 PMMA 18.000 -2.219
3 -22.475 26.000 18.000 -3.180
4 - Image Infinity - 23.937
The layout of the lens is shown in Figure 15. Key performance metrics, including field
curvature, distortion, spot diagrams, and MTF, are shown in Figure 16. The spot diagrams show
the lateral color caused by using a single refractive element. Given the narrow spectral profiles
for the red, green and blue, each can be corrected for lateral location individually in software.
The MTF for the system is also shown for 530nm and the polychromatic case which includes the
peaks for the red and blue wavelengths. With the tendency of looking straight forward, the low
field angles are more important than the edge fields. The distortion is also of note for a design
such as this, and is not atypical of expectations. It is not of as much concern as it can be
corrected in rendering and does not have significant appearance when using the Gear VR system.
Distortion characteristics will be something useful as a diagnostic in the illumination model to
determine that everything has been set up properly.
Page 15 of 57
Figure 15. Viewing Lens Layout.
a) b)
c) d) Figure 16. a) Field curvature and distortion plot. Scale on field curvature is ±3mm and distortion
is ±30%. b) RMS spot sizes for fields of 5, 10, 15, 20, 25, 30, 35, 40, 45, and 48 degrees HFOV.
Scale is 1000 microns. c) Monochromatic MTF plot at 530nm for all fields. d) Polychromatic MTF
plot for 458, 530 and 612nm. Pupil diameter set to 4mm for all analysis.
One of the advantages to setting the system up in this way is that performance is compared at the
display plane. The designer knows the pixel size, pixel spacing, and curvature of the display.
Resolution is evaluated based on the size and spacing of the individual display pixels and
Page 16 of 57
requires no assumptions about the performance or behavior of the human eye. The distortion
curve from Zemax gives the information to pre-distort the image so that it appears undistorted.
Chromatic aberration can be corrected in a similar fashion. Field curvature plots appear as
variation from the display plane and provide comparison with which most designers are familiar
with, such as a camera lens imaging onto a sensor.
CAD Creation
In order to create the housing for the system, SolidWorks was used starting with a rectangular
block design. As seen in Figure 5, the screen side has circular cutouts that allow the light from
the display to reach the optics. A conical cutout is used immediately contacting the lens. An
additional cutout is in the middle of the housing, likely for light-weighting purposes. On the user
side of the lens, a circular retaining mount holds the lens in place. These features are shown in
detail in Figure 17. All features were measured using a pair of Mitutoyo calipers.
The existing lens surfaces from the Zemax design were maintained as clear apertures. A 1.0 mm
wide flange was added to the outside of the lens to assist in mounting. A 0.050 mm gap was left
on any side of the flange for placement of adhesive. There are no plans to include this adhesive
in the model.
A single IPD value of 66mm was chosen for the spacing between the optical axes for the two
eyes. This value was within the specified performance range of the IPD adjustment. By using
mirroring features in SolidWorks, this could be easily updated to reflect a different IPD value.
On the user side, a rounded section creates a facial interface that can be seen in Figure 5. That is
not included here as it is assumed that the majority of stray light will come from the housing
features between the display and optics rather than the facial interface.
Page 17 of 57
a)
b) c) Figure 17. a) Measured dimensions of internal portion of the rig housing. Units in mm.
Highlighted features are revolved around the line 33mm from the centerline. b) Top cross section
view showing optics held in place. c) Isometric cross section view highlighting the lightweighting
cuts in the housing.
Preliminary LightTools Model Verification
First, the STEP file from SolidWorks was imported into LightTools. All surfaces were set to
Mechanical Absorbers and perfectly absorb incident light. The lenses were made in native
LightTools geometry using the Quick Lens command. Flanges were added and all lens surfaces
were set 100% transmitting or TIR mode. Later in the analysis process, the plastic housing will
include some reflectance and scattering and the lenses will act like bare surfaces and exhibit
Fresnel reflections after the initial model performance has been verified. Figure 18 shows two
isometric views of the combined geometry in LightTools.
Page 18 of 57
a) b) Figure 18. LightTools geometry of lenses and housing. No source or receivers have been added.
Lenses are shown in pink for transmitting geometry and the housing is shown in light purple.
Image a shows the side closest to the Note 4 and image b shows the side closest to the user.
The lenses were designed out of PMMA. Before proceeding with the rest of the model, the
parameters of default PMMA in LightTools were analyzed by extracting the material properties.
Figure 19 shows the intrinsic transmittance of PMMA in LightTools along with index of
refraction. As a sanity check, the extrinsic transmittance of a 3mm thick cast PMMA sheet from
polymer manufacturer Evonik is shown as well. The full parameters of this PMMA sample are
not known, so it is being used to make sure nothing is severely wrong with the default
LightTools PMMA parameters. Taking into account the Fresnel reflections from both surfaces
(~8% total), the spectrum over the visible appears correct in LightTools. The index of refraction
also seems quite reasonable.
Page 19 of 57
a) b)
c) Figure 19. a) Intrinsic transmittance for given thickness in LightTools and b) extrinsic
transmittance of cast Acrylite® PMMA from Evonik [24]. Of interest is the FF (gray) line as that
material does not have the UV blocking additive that the OP3 (purple) line has. c) Index of
refraction for standard PMMA in LightTools.
The source in the LightTools model was created next. A 66mm horizontal by 75mm vertical
rectangular source was added and placed to match the center of the source with the optical axis
of the right eye. Only the surface facing the optics was set to emit rays. No surface properties
were added to the geometry and the material was set to air. The selection of air as the material
was to avoid any rays getting internally reflected for n>1. The measured spectral data from the
Note 4 panel was added into the source. The spectrum was cutoff where the value was less than
1% of maximum to avoid creating rays with low power.
A block of glass was added in front of the display to simulate the display coverglass. One side
was set have the coating to correct for the display luminance and spectral variations over viewing
angle. Figure 20 shows this coating performance in transmission and absorbs rays that aren’t
transmitted. For AOIs beyond 60 degrees, the values at 60 degrees AOI are used. The other side
was set to account for Fresnel reflectance and transmittance. This was done as setup for stray
light analysis in the system later on but will not impact the initial model verification. It is
assumed that any Fresnel effects from the side of the coverglass internal to the display are
already included in the measurement results. The glass type was selected as Schott BK7 because
the coverglass material is unknown. The source was set to be Lambertian and emission angle
restricted to be from 0 to 90 degrees from source normal to emit into one full hemisphere.
Page 20 of 57
Figure 20. Coating transmittance used to model the screen performance over viewing angle.
The user sets the total flux from a source in LightTools. The program then automatically
calculates ideal luminance for Lambertian sources. To make the display the correct brightness,
the equivalent luminous flux was set to 5.1318 lumens, which resulted in 330 nits of brightness
at 0 degrees AOI. No modifications were made for the spatial uniformity of the source. Once
complete, the source was duplicated and placed in front of the left eye in the same manner.
Eye Model Implementation
Next, it is necessary to include an eye model to analyze the performance once passed through the
entire system. Zemax and CodeV offer paraxial lens equivalents that some designers use when
tracing from display to retina. LightTools does not offer this option and requires the construction
of an eye model from real geometry. As many eye models exist [25], one could also consider
designing a replacement lens for use in the illumination model with a stop at the first element to
represent the pupil. This may be a good option as some eye models, such as the Arizona eye
model, include off-axis aberrations that may not be necessary for the analysis.
In order to compare the MIL-HDBK-141 Eye Model [26] and the Arizona Eye Model [25], the
prescriptions were first put into Zemax for sequential performance characterization. The
Arizona Eye Model changes with accommodation distance to simulate the performance of the
eye as the lens changes shape. This is advantageous because it can be easily parameterized in
LightTools and one variable used to control accommodation. Additionally, neither of these
models include gradient index materials like some newer eye models. The lack of gradient index
materials makes the implementation straight forward. The prescriptions used for these two
models are shown in Table 7 and Table 8. Both lenses were set to have the object at infinity,
matching the designed VR image distance.
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Table 7. Prescription for MIL-HDBK-141 Eye Model [26]. All units in mm.
Surface Radius Thickness Material Semi Diameter Conic
0 - Object Infinity Infinity Infinity
1 - Cornea 7.980 1.150 367000 4.152
2 - Aqueous 6.220 2.390 336000 3.253
3 - Lens (stop) 10.200 4.060 420482 1.775
4 - Vitreous -6.170 17.150 337000 3.480
5 - Image -11.100 - 10.739
Table 8. Prescription for Arizona Eye Model for no accommodation (focused at infinity) [25]. All
units in mm.
Surface Radius Thickness Material Semi Diameter Conic
0 - Object Infinity Infinity Infinity
1 - Cornea 7.800 0.550 377571 4.142 -0.250
2 - Aqueous 6.500 2.970 337613 3.662 -0.250
3 - Lens (stop) 12.000 3.767 420519 1.782 -7.519
4 - Vitreous -5.225 16.713 336611 3.319 -1.354
5 - Image 13.400 - 11.553
Both of these models were set to include fields up to 50 degrees HFOV. The MIL eye has a
focal length of 17.09mm, while the Arizona eye has a focal length of 16.50mm. Each lens was
set to have a 4mm entrance pupil diameter. The MIL eye only includes dispersion for the
crystalline lens, whereas the Arizona eye includes dispersion for all elements. The Arizona Eye
Model includes the use of aspheric terms while the MIL eye is all spherical. Each of these
includes the retina as a curved image plane. Layouts are shown in Figure 21.
a) b) Figure 21. Layouts for a) MIL-HDBK-141 and b) Arizona Eye Models. Scale bar is 4.0mm for
each.
In order to compare performance of the lenses, spot diagrams and MTF plots were generated for
comparison. These are shown in Figure 22 and Figure 23.
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a) b) Figure 22. Spot diagrams for a) MIL-HDBK-141 and b) Arizona Eye Models. Fields are from 0 to
50 degrees in increments of 10 degrees. Scale bar is 400 microns. F, d, and C wavelengths used for
analysis.
a) b) Figure 23. Polychromatic Diffraction MTF plots for a) MIL-HDBK-141 and b) Arizona Eye
Models. Diffraction limit shown as black line.
The Arizona Eye Model shows improved performance compared to the MIL-HDBK-141 eye.
Over the FOV of interest, the performance is not drastically different between these two lenses
and either may be suitable for analysis. For additional comparison, field curvature and distortion
plots were generated. Relative illumination plots were also created. These are shown in Figure
24 and Figure 25, respectively.
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a) b) Figure 24. Field curvature and distortion plots for a) MIL-HDBK-141 and b) Arizona Eye Models.
Scale on field curvature is ±2.0mm and scale on distortion is ±50%.
a) b) Figure 25. Relative illumination plots for a) MIL-HDBK-141 and b) Arizona Eye Models.
The Arizona Eye Model shows less field curvature and astigmatism than the MIL Eye Model.
Axial chromatic aberration is improved in the Arizona Eye Model, but is still present. Both
models show significant distortion at the higher field angles, with the Arizona Eye Model
showing improvement over the MIL model. Relative illumination is slightly worse for the
Arizona Eye Model at 80% for the full field.
With the comparison completed, the MIL and Arizona Eye Models were created in LightTools.
Each component was created as a lens element and touching interfaces were made to have
optical contact. All extra surfaces were set as optical absorbers. The retinas were implemented
as curved image planes. The layouts are shown in Figure 26. For the image planes, the size and
number of bins are set by the user. The size of the image plane will restrict the FOV for the
receiver. The receiver area is subdivided into bins and the rays incident on each bin are summed
for power, luminance, and chromaticity. With more bins for the same simulation, the ability to
resolve fine detail is increased, but the statistical error for the raytrace is higher since less
samples are made within each bin. Reporting the error from the raytrace provides an estimate on
the fidelity of the results. The revised MIL eye and the Arizona eye both had an illuminance
-50-2.00 00.00 502.00
Millimeters Percent
+Y +Y
Field Curvature Distortion
T ST ST S
Mil Hdbk Eye Model Report.zmxConfiguration 1 of 1
Field Curvature / F-Tan(Theta) Distortion
5/3/2015Maximum Field is 50.000 Degrees.Wavelengths: 0.486 0.588 0.656
-50-2.00 00.00 502.00
Millimeters Percent
+Y +Y
Field Curvature Distortion
T ST ST S
Arizona Eye Model Report.zmxConfiguration 1 of 1
Field Curvature / F-Tan(Theta) Distortion
5/3/2015Maximum Field is 50.000 Degrees.Wavelengths: 0.486 0.588 0.656
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mesh with 401x401 bins at 26.8mm square, thus slightly different sized images based on the
different focal lengths.
a) b) Figure 26. LightTools layouts for a) revised MIL-HDBK-141 Eye Model and b) Arizona Eye
Model.
In order to update the eyes to match the model, the receivers were switched from radiometric to
photometric quantities. An initial forward ray trace showed that the system was working
properly and the illuminance mesh boundaries were updated to a larger size to capture the edges
of the field. However, when tracing from the display to the eye, only a small percentage of rays
were successfully propagating to the retina. This is because the display is spatially large
compared to the 4mm aperture of the eye. Additionally, the display is emitting in a 90 degree
cone from the normal, so many rays do not have the opportunity to pass all the way to the retina.
A backwards ray trace was then set up to trace from the eye to display and then update the
performance at the retina based on where it interacted with the display. An aim region was
selected on the eye to aim only at the optic and not send extraneous rays out to be absorbed by
the housing. The receiver was set to 171x171 bins at 34mm square with smoothing off.
A checkerboard on the display added such that each square was 1.5x1.5mm. An additional circle
mask of 24.630mm radius was added to match the design field of view of the lens to provide
more delineation as to the boundary of the system. With all optical geometry set to have 100%
transmission or TIR, the ray power threshold was set to 1% for tracing. The ray trace was run
backwards with 2.147 billion rays, as previously performed, for comparison. LightTools is
limited to 2.147 billion rays based on its random number generating algorithm. These ray traces
took approximately 1.25 hours each on a laptop.
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a) b)
c) d) Figure 27. On-axis illuminance meshes for a) revised MIL-HDBK-141 Eye Model and b) Arizona
Eye Model. 30 degree off-axis illuminance meshes for c) revised MIL-HDBK-141 Eye Model and d)
Arizona Eye Model.
In comparing the performance, both models appear very similar to each other. For additional
comparison purposes CIE meshes, or 2D plots, were included in the same analysis. These are
shown in Figure 28.
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a) b)
c) d) Figure 28. On-axis CIE meshes for a) revised MIL-HDBK-141 Eye Model and b) Arizona Eye
Model. 30 degree off-axis CIE meshes for c) revised MIL-HDBK-141 Eye Model and d) Arizona
Eye Model.
The plots show 100% contrast since no scattering or Fresnel reflections were present in the
simulation. The expected lateral chromatic aberration from the viewing lens is visible in these
plots. The MIL and Arizona Eye Models exhibit axial chromatic aberration but not a very
pronounced lateral chromatic aberration. The advantage to using the Arizona Eye Model is the
wide field of view performance that can assess the entire system performance at once. The
disadvantage to the Arizona Eye Model is that it does not offer high resolution, contains
chromatic aberration, and has significant distortion. Having a lens without these issues will
allow assessment of the headset optical system itself without introducing any error. This is the
motivation for creating an “Ideal” Eye Model and will be discussed in detail in later sections.
Stray Light Analysis
With representative performance from the display and the viewing optics in the model,
representative performance from the plastic housing was the final item for inclusion. All of the
surfaces between the display and the user are black in color. Most of the surface was textured
and, when illuminated with a green laser beam, produced a very diffuse reflection. Only one
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surface had a specular appearance and it was around the retaining ring for the lens. This single
surface is shown in Figure 29.
Figure 29. Designation for black specular housing surface, shown in gray and highlighted using
green arrow. Housing is shown in dark red, lens is shown in magenta, Arizona Eye Model shown in
gold.
Visibly rough black plastic surfaces were set to Lambertian scattering with 8% reflectance. For
the specular surface, it was left as a specular reflector of 8% reflectance. This was an
assumption based on the estimation that the black surfaces would be 5-10% reflective.
For this analysis, a wide field of view was desired. Using the 1.5x1.5mm checkerboard pattern,
the resulting stray light will appear in the portions of the checkerboard that are dark. This makes
a good case for using the Arizona Eye Model for this simulation. Additionally, the detector was
switched from linear to logarithmic to simulate the detection method of the eye. The dynamic
range of the eye for a single scene varies in the literature from 2.4 orders of magnitude [27] to 6
orders of magnitude [28]. A value of 4 orders of magnitude was selected as an estimate since it
was between these values. The ray tracing power threshold was also dropped to 1x10-6 to ensure
the rays would arrive properly at the detector for this thresholding.
When analyzing stray light, one can use selection criteria on the ray paths to see specific surface
interactions. As a preference for this setup, five different ray traces were run in order to compare
the contributions step by step. In the first ray trace, the baseline performance was set. In this
model, the viewing lens geometry was set to transmitting and all housing parts remained as
mechanical absorbers. In the second ray trace, Fresnel reflectance/transmittance was added to all
viewing lens surfaces – including the flange and edge. Ray splitting behavior was set to
probabilistic to maintain the “one ray in, one ray out” approach. In the third ray trace, the
Fresnel performance remained on the viewing lens and the specular reflection was added to the
retaining lens surface while the rest of the housing remained as a mechanical absorber. In the
fourth ray trace, the Fresnel performance remained on the viewing lens and the Lambertian
reflection was added to the whole housing except the retaining ring, which remained as a
mechanical absorber. In the fifth and final ray trace, Fresnel performance was on the viewing
lens, the retaining ring exhibited specular reflectance, and the rest of the housing exhibited
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Lambertian reflectance. The illuminance meshes are shown in Figure 30 and Figure 31. Each
simulation ran with 2.147 billion rays in reverse ray trace mode, taking approximately 1 hour
each to complete.
For the first ray trace (Figure 30), the expected behavior is observed with illuminance seen only
in the white portions of the checkerboard. The black portions have illuminance below the
threshold, but in reality are 0 lux. The boundary is clear on the edge of the field. For the second
case (Figure 31a), stray light occurs in the center of the field of view from the Fresnel reflections
of the viewing lens and the coverglass from the screen. For the third case (Figure 31b), the
specular reflectance on the retaining ring adds illumination at the boundary of the field as
expected. Fortunately, this does not creep too far into the FOV, but is still present. For the
fourth case (Figure 31c), the Lambertian scattering adds noise outside of the region where the
Fresnel reflections contribute. There is a small ring section that does not appear to have stray
light from either effect. In the fifth simulation (Figure 31d), the stray light contributions all add
together to produce the final expected result.
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Figure 30. Baseline illuminance mesh for stray light analysis. All geometry set as 100%
transmitting for optical components and mechanical absorber for housing surfaces.
a) b)
c) d) Figure 31. Illuminance meshes for stray light analysis using the Arizona Eye Model. All meshes
include Frensel transmittance/reflectance on the viewing lens with probabilistic ray splitting. a)
Fresnel on lens only. b) Black specular retaining ring surface added. c) Black Lambertian scatter
on mechanical housing. d) Black specular retaining ring and black Lambertian scatter on housing
combined. All charts set to a maximum luminance of 19.4 lux and a minimum of 1.94x10-3.
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For ease of comparison, the modulation contrast was calculated at 0 degrees and 30 degrees FOV
for all five cases. The results are shown in Table 9. The largest cumulative effect occurs at the
edge of the field of view. There is significant benefit from eliminating the contribution of the
Fresnel reflections from the lens, like the use of an AR coating.
Table 9. Modulation contrast performance for the various stray light cases.
Model Case 0 Degrees 30 Degrees 48 Degrees
None 100.0% 100.0% 100.0%
Lens Fresnel Reflection Only 98.5% 100.0% 99.9%
Black Specular Retaining Ring + Lens Fresnel 98.5% 100.0% 98.5%
Lambertian Scattering Housing + Lens Fresnel 98.5% 99.8% 99.8%
Black Specular Retaining Ring + Lambertian
Scattering Housing + Lens Fresnel
98.5% 99.8% 98.4%
For a future simulation, the expected scattering from the lens optical surfaces could be included
based on assumed molding conditions or the measurement of surface roughness with a white
light scanning interferometer. The modeling of the diffuse reflecting surfaces could also be
improved through measurements, although that could be time consuming or costly.
Ideal Eye Motivations
For virtual reality, one can think of the example of recreating a real world scene inside the VR.
The objective is to make the virtual scene appear as realistic as possible. The scene presented to
the user is the result of all interactions between the display, optics, and mechanical features of
the virtual reality headset.
In the previous examples, the MIL and Arizona Eye Models were used to “measure” the
performance of the VR system. As with any measurement, the measurement device must have
less intrinsic error than the required fidelity of the measurement. Likewise, the replacement eye
model used for assessment must have very little error. For the lens system that goes in place of
the eye, this would ideally have an infinitesimally small points [29], have equal relative
illumination for all fiend angles, and be free from distortion and chromatic aberration.
The primary reason for wanting an “Ideal eye replacement” is that it gives the designer a clear
understanding of what is occurring in the VR headset. A perfect VR system analyzed using the
Arizona Eye Model would still include all the clinical levels of aberration and distortion. It
would be difficult for the designer to understand if distortion correction on the image was being
applied properly. It would be difficult for the designer to see if fine features were being
obscured since the Arizona Eye Model is not diffraction limited.
The designer should also not design the system to counteract the aberrations present in the
Arizona Eye Model. When the eye looks at a scene in the real world, all of the aberrations from
the eye are applied to the image. The brain is expecting these aberrations and compensates
appropriately for them. Since most people have eye performance that varies from the Arizona
Eye Model, it doesn’t make sense to attempt to compensate specifically for the model. This also
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does not take into account cases of myopia or hyperopia, as those conditions also influence the
appearance of aberration in the eye by acting as defocus of the imaging plane [29]. This is not to
say that the Arizona Eye Model is not useful in illumination and system design, but it is to say
that alternative eye models provide significant analysis benefit. The purpose of the Ideal eye is
to create a tool that allows analysis of the rest of the system without contributing error that is
significant in the analysis.
Implementation of this scheme varies based on sequential or non-sequential raytracing codes. In
Zemax, the evaluation could be performed by reversing the existing system such that the object
is the display. A replacement for the eye would then be added at the appropriate location and the
image would be representative of the image on the retina. This eye replacement would simply be
a paraxial lens with a user specified focal length. In LightTools, this is problematic because the
chief and marginal rays are not calculated from the model. Thus, LightTools has no capability
for a paraxial lens.
Using a variety of designs that are not physically realizable, Ideal Eye Models can be designed in
sequential lens design software. Diffraction is still present in the sequential software, but is not
calculated in LightTools. This means for the illumination simulation that spot size should be the
key criteria even though other optical performance parameters will be analyzed. For an
illumination eye model, the goal will also include minimizing the number of surfaces involved
for less interactions during ray tracing.
Narrow Field Ideal Eye
In order to simulate the eye, it is good to have the stop of this lens system as the first element of
the system to clearly define the eye relief being used in the system. The design objectives for
this are to create a model with low distortion, a flat image plane, no chromatic issues, and
diffraction limited performance since the eye can achieve this with a 2mm diameter pupil [30].
It is useful to have a narrow field of view eye because all rays from the simulation are spread
over the field of view when reverse raytracing. A narrow field eye allows gathering of precise
performance at a specific viewing angle. A wide field eye model allows viewing of stray light
and an overview of the complete image as previously demonstrated. Thus, these two types of
models complement each other nicely for system analysis.
For assessing the system performance, luminance, color, stray light, resolution, distortion,
chromatic aberration, and contrast performance are all of key interest. Creating an eye that is flat
fielded, or acts like a spatial luminance meter, will allow assessment of luminance and luminance
fall off throughout the system. A lens system without chromatic aberration will allow for exact
color analysis. Using the size of the cones of the eye allows a strict criteria to be set for
distortion performance. The use of non-absorbing, non-scattering materials for the lens, along
with perfect absorbers for mechanical features, enables the assessment of stray light cause by the
VR system. All of these can be accomplished to make excellent analysis tools.
To start this, the CodeV lens database was searched for a starting candidate for the design. Japan
Patent 61_4088 was selected and the design was input into Zemax. The lens was scaled to
16.27mm effective focal length and operated at f/4.06. This five element lens had a 20 degree
Page 32 of 57
diagonal FFOV as designed. The prescription is shown in Table 10 and the initial layout is
shown in Figure 32.
Table 10. Starting prescription based on JP 61_4088. All units in mm.
Surface Radius Thickness Material Semi Diameter
0 - Object Infinity Infinity Infinity
1 - Stop 4.330 0.693 589610 2.095
2 17.640 0.016 2.068
3 3.494 0.326 806409 2.021
4 2.257 0.815 618634 1.814
5 8.300 0.244 1.790
6 17.600 0.392 720420 1.752
7 2.606 3.470 1.582
8 8.413 0.354 658338 2.235
9 18.877 8.272 2.236
10 - Image Infinity - - 2.985
Figure 32. Starting lens layout based on JP 61_4088.
Making the lens achromatic across the visible from 380-780nm can be challenging with real
glasses. However, since this is an analysis tool the lens can be designed at a single wavelength.
The resulting index of refraction at the design wavelength can be applied to all other
wavelengths, giving the lens the same performance across all wavelengths. In this manner, the
d-line at 587.6nm was selected. This wavelength was set in the system and fields of 0, 7, and 10
degrees were set for initial lens performance. Spot diagrams, MTF, field curvature, distortion,
and relative illumination plots are shown in Figure 33.
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a) b)
c) d) Figure 33. a) Spot diagram for JP 61_4088 at 0, 7, and 10 degree fields. Scale is 200 microns. b)
Diffraction MTF for JP 61_4088. c) Field curvature and distortion plots for JP 61_4088. Scale for
field curvature is ±0.020mm and scale for distortion is ±1%. d) Relative illumination plot for JP
61_4088.
One of the reasons this lens was selected was the low distortion performance as a starting point.
To begin the optimization process, the model glasses were changed to real Schott glasses with
Zemax making the automatic selection. Typically, using the 0, 0.7 and 1.0 fields is sufficient,
but for this design 12 evenly spaced field points were used to aid in optimizing for spot size
without creating larger spots in between the sample points. The maximum field was set to 15
degrees.
Ophthalmic research has shown the mean peak acuity of 8 subjects was found to be 67.2 cycles
per degree with a mean receptor spacing of 2.5 microns for the fovea [31]. The highest peak
acuity of the study was 84.5 cycles per degree. This gives some notion of performance
requirements for spot size and distortion. Applying this to the 15 degree HFOV, the distortion
target should be less than 0.04% if applied across the entire field. A value of 0.01% was selected
at 0.25, 0.50, 0.75 and 1.0 fields. A default merit function was loaded for peak-to-valley spot
size, including constraints on glass and air thicknesses. Correction for specific aberrations was
not included. Optimization was first allowed for all radii and the back focal distance. Next, all
other thicknesses were allowed to vary. Finally, the glasses from all five lenses were allowed to
be substituted with other glasses from the Schott catalog. For the glass selection, this could have
been done using a model glass with any index the program would like. An initial optimization
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using Hammer optimization to allow for the glass substitution was performed. This was
followed by approximately 2000 cycles of global optimization. The design parameters and
results are listed in Table 11 and the final prescription is listed in Table 12.
Table 11. Design specifications and results for the Ideal narrow field eye.
Item Specification Result
Effective focal length (mm) 16 Same
Entrance pupil diameter (mm) 4 Same
Stop location Surface 1 Same
First optical surface Surface 2 Same
Object / virtual image distance (m) Infinity Same
Design wavelength (nm) 587.6 Same
Distortion at any field point (%) <0.01 Same
Spot radius diameter <Airy Disk Same
Minimum glass center thickness (mm) 0.050 Same
Maximum glass center thickness (mm) 5.000 Same
Minimum glass edge thickness (mm) 0.050 Same
Minimum air center thickness (mm) 0.050 Same
Maximum air center thickness (mm) 1000 Same
Minimum air edge thickness (mm) 0.050 Same
Table 12. Prescription for Ideal Narrow Eye Model. All units in mm.
Surface Radius Thickness Material Semi Diameter
0 - Object Infinity Infinity 0.000
1 - Stop Infinity 0.001 2.000
2 14.260 4.931 SF11 2.040
3 8.501 0.159 2.448
4 12.272 3.088 FK3 2.470
5 -6.645 4.955 N-LAK33A 2.914
6 -16.869 3.457 4.187
7 30.201 1.387 SK15 5.274
8 -16.401 13.211 5.278
9 -10.062 0.050 LASF35 4.101
10 -1019.157 0.050 4.264
11 - Image Infinity - - 4.268
One of the objectives was to find an all spherical solution. This was achieved for this lens
design. Some of the glasses selected are a bit unique because of their high refractive index. The
final element has also moved closer to the image plane to act like a field flattener. The layout for
the lens is shown in Figure 34 and the performance of the lens is shown in Figure 35.
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Figure 34. Layout for Ideal Narrow FOV Eye Model.
a) b)
c) d) Figure 35. a) Spot diagram for Ideal Narrow FOV Eye Model at 0, 3, 6, 9, 12, and 15 degree fields.
Scale is 10 microns. b) Diffraction MTF for Ideal Narrow FOV Eye Model. c) Field curvature and
distortion plots for Ideal narrow FOV Eye Model. Scale for field curvature is ±0.002mm and scale
for distortion is ±0.01%. d) Relative illumination plot for Ideal Narrow FOV Eye Model.
The key design objectives have been achieved with this lens, including spot sizes smaller than
the Airy disk and diffraction limited performance. The distortion is very good and the field
curvature is nearly non-existent. One item that was not constrained in the design was the relative
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illumination. At the edge of the field, the relative illumination is 87%. In order to counteract
this issue, another coating can be used on a flat plate in front of the lens. This profile is shown in
Figure 36. As with the previous coatings, the power for the source will need to be increased to
counteract the lost transmission.
Figure 36. Angular dependence for the relative illumination corrector coating for the Ideal narrow
eye. Corrector coating is equal for all wavelengths (no spectral dependence).
The design was then entered into LightTools using the Quick Lens function to build each of the
individual elements. The cemented interface between elements 2 and 3 was made by declaring
the surface as optically contacted. A user defined material was created for each element to have
a constant index matching nd for the glasses in the optimization. Each material was non-
absorbing and the lens surfaces were set to 100% transmitting. A block of air was added at the
front interface with the relative illumination corrector coating applied. An absorbing thin skin
was added via skinned solid in sheet mode to allow only light through the optics to reach the
detector. This blocks light that did not pass through the optics from hitting the detector plane.
To verify the performance of the eye model, a Lambertian source was placed in front of the lens.
Source power was set to 1 W over the entire sphere, placed 0.1mm in front of the lens aperture,
and oversized to 8mm circular diameter to fully illuminate the lens. The wavelength was
selected as 550nm. Figure 37 shows the performance of the lens with and without the relative
illumination corrector coating in place. As expected, the illuminance at the retina is constant
across the field. With this lens now flat fielded, it can be used to compare the performance of a
simulated scene without introducing error that is significant to the simulation.
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Tran
smit
tan
ce
Field angle (deg)
Relative Illumination Corrector - Narrow Ideal Eye
Page 37 of 57
a) b) Figure 37. Illuminance mesh of narrow Ideal eye a) without and b) with relative illumination
corrector coating. Source power is the same for both measurements. Maximum scale is 2.2x105 lux
for both plots.
Once the Ideal lens was complete, it was placed into the system LightTools model. The lens was
positioned such that the aperture stop was 10mm from the rear lens vertex – or coincident with
the iris location for the Arizona Eye Model. This is shown in Figure 38.
Figure 38. Complete system in LightTools with Narrow FOV Ideal Eye Eodel.
With the eye models in place, the receiver size was changed to be 4.212mm square
corresponding to a horizontal FFOV of 15.0 degrees. The model was then rotated in the
horizontal plane to 0, 15, 30, and 45 degrees. Each ray trace took approximately 60 minutes on a
laptop, yielding 75 million backwards traced rays for about 4.75% error. The receiver was set to
401x401 pixels and did not include smoothing. Figure 39 through Figure 42 show these various
meshes for illuminance and color.
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a) b) Figure 39. a) Illuminance mesh and b) CIE mesh for system with Ideal eye looking on-axis.
Illuminance mesh maximum is 1.9 lux.
a) b) Figure 40. a) Illuminance mesh and b) CIE mesh for system with Ideal eye looking 15 degrees off-
axis. Illuminance mesh maximum is 1.9 lux.
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a) b) Figure 41. a) Illuminance mesh and b) CIE mesh for system with Ideal eye looking 30 degrees off-
axis. Illuminance mesh maximum is 1.9 lux.
a) b) Figure 42. a) Illuminance mesh and b) CIE mesh for system with Ideal eye looking 45 degrees off-
axis. Illuminance mesh maximum is 1.9 lux.
The Ideal Narrow Eye Model shows its utility through this series of analysis. First, the
illuminance change from the system is visible and there is no contribution from the Ideal eye.
Second, the resolution of this is very good. The measurement at 45 degrees shows this in
particular because of the lateral color and distortion coming from the optical system and not the
eye model. Third, this model allows the peak error estimate to be reduced significantly. Here,
5% error was found during a 60 minute ray trace. This error can be additionally reduced by
tracing more rays. Alternatively, if ray trace time is a concern, this be reduced to 15 minutes of
ray tracing time by going to 201x201 receiver bins. Based on the data, the images were stitched
together in Adobe Photoshop for illustrative purposes. One could automate the system to stitch
the data together using a macro or other piece of analysis software like MATLAB. The images
in Figure 43 show the performance of the whole system with excellent resolution.
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Figure 43. Stitched illuminance mesh (top) and CIE color mesh (bottom) from the Ideal eye model.
Scales not adjusted for illuminance mesh during stitching operation.
Color and Relative Illumination Analysis
With the Ideal Narrow FOV Eye Model in LightTools, the color and relative illumination
performance of the display and viewing optics together can be analyzed without any contribution
from the eye model. In previous analysis, illuminance and CIE mesh data were collected. For
this analysis, the same will be performed but with slight modifications. At this stage, Fresnel
reflectance/transmittance was added to the viewing lens. This used probabilistic ray behavior
rather than splitting the rays at the interfaces for “one ray in, one ray out” performance. This
represented the performance of just the lens and display together. Contributions from the
housing will be assessed in the next section.
Since continuous color and relative illumination performance are desired, the checkerboard
pattern was removed to make the source solid white. Backwards raytracing will still be used for
this simulation. The retinal receiver size is reduced to be 0.4mm in the vertical direction and
8.572mm wide since a 1D plot is desired rather than 2D. This will increase the efficiency of the
ray trace and utilize the full 30 degrees FFOV capability of the lens. The detector array was set
to 201x1 pixels to generate this radial plot. A ray trace of 100M rays took approximately 3
minutes and yielded less than 2% error. With the Ideal Narrow FOV Eye Model now operating
at 30 degrees full horizontal FOV, the ray trace was run at 15 degrees and 45 degrees relative to
the optical axis of the viewing lens.
Here, the low distortion of the Ideal Eye Model provides another benefit. The virtual screen
appears at infinity, so the spatial locations on the receiver can be directly converted into field
angles. The illuminance has already been corrected by the Ideal eye’s relative illumination
corrector coating, so the data requires only normalization by the 0 degree illuminance. The CIE
mesh in LightTools was reported in CIE 1931 color space. In order to compare in the more
uniform CIE 1976 color space, the results were converted from CIE 1931 x and y values to CIE
1976 u’ and v’ coordinates. This allows a more useful value of Δu’v’ reported for color shift.
Equations 3, 4 and 5 show this process.
Page 41 of 57
𝑢′ =4𝑥
−2𝑥+12𝑦+3 (3)
𝑣′ =9𝑦
−2𝑥+12𝑦+3 (4)
∆𝑢′𝑣′ = √(𝑢𝑟𝑒𝑓′ − 𝑢′)2 + (𝑣𝑟𝑒𝑓
′ − 𝑣′)2 (5)
For this case, the reference white point was determined by averaging the u’ and v’ values from 0
to 1 degrees AOI. The relative illumination and color difference are shown in Figure 44. The
relative illumination shows good performance better than 90% out beyond 44 degrees. Beyond
44 degrees, there is a sharp fall off. This fall off may be caused by the chromatic aberration at
the edge of the field where longer wavelengths will not be present. The plot was restricted to 48
degrees HFOV, corresponding to the specified FOV of the system. The color difference from
on-axis to the edge of the field is less than 0.005, which is also very good performance. The
simulation was performed using only the white image color spectrum. This simulation could
also be performed using the red, green, and blue channels individually as well.
Figure 44. Plot of relative illumination and color difference from the simulated system. Relative
illumination shown in red on the primary axis, color difference shown in blue on the secondary
axis.
Wide Field Ideal Eye
The motivations for making an Ideal Narrow FOV Eye apply the same to making an ideal eye
with a wide field of view. In this case, the FOV of the Ideal Eye should exceed the per eye FOV
of the VR system. The same constraints apply – low distortion, diffraction limited performance,
no chromatic aberration, and a flat image plane.
One of the techniques for mitigating distortion and chromatic aberration is to render the opposite
distortion and chromatic aberration introduced by the lens. The user then sees an image that
0.000
0.005
0.010
0.015
0.020
0.025
00.10.20.30.40.50.60.70.80.9
1
0 10 20 30 40Δ
u'v
' (b
lue
line)
No
rmal
ized
Illu
min
ance
(re
d li
ne)
Viewing Angle (Deg)
Simulations Over Viewing Angle
Normalized Illuminance Color Difference
Page 42 of 57
does not appear to have either distortion or chromatic aberration. The desktop Oculus Rift does
this as an example, and a sample image rendered to the display is shown in Figure 45. By having
a wide angle lens that has practically no distortion or chromatic aberration, the correction
performance can be evaluated in LightTools. This is one of the key benefits for making this
Ideal wide angle lens.
Figure 45. Sample image rendered to Oculus Rift showing distortion and chromatic aberration
correction [32].
In the case of the Ideal Narrow FOV Eye, the design started with the patent lens and was
optimized using real Schott glasses. After monochromatic optimization, the d-wavelength index
of the glass was applied to all wavelengths (i.e. each glass was made dispersionless).
Maintaining similar performance characteristics over a wide FOV will be very challenging, so
one option is to allow dispersionless glasses of n>1 for all elements. The index of refraction will
have no upper numerical limit.
This enables a much wider range of solutions. Looking at the Narrow Ideal Eye Model,
analyzing 12 different versions of this eye model provide insight into how the numerical
ficticious glasses help to create the final eye model. The patent lens was adapted into twelve
cases – 4, 5, and 6 elements; 15 and 30 degrees HFOV; and real Schott glasses and numerical
fictitious glasses. For the case of 4 elements, one element of the doublet was removed. The
same merit function was used with a default merit function to minimize RMS spot size, a focal
length of 16mm, distortion < 0.01%, and spacing constraints as listed in Table 11.
Using the same merit function used to find the Ideal narrow FOV lens, each lens was Hammer
and global optimized in a similar fashion. Figure 46 shows these results.
Page 43 of 57
Figure 46. Plot of Merit Function value. Results show much quicker convergence to a solution
using fictitious glasses.
When using fictitious glasses, performance with 4 elements is near the performance limit with 15
degrees HFOV where it takes 6 elements of real glasses to match the performance. For 30
degrees HFOV, performance with 5 elements is near the best possible while the real performance
with 6 elements is still less than ideal. This provides the motivation for moving to fictitious
glasses with n>1 such that there are no issues with the program for indices less than 1. This will
allow the best solution with the minimum number of elements possible to speed up the non-
sequential ray trace.
Having demonstrated the utility of the fictitious glasses, design work on the Ideal Wide FOV
Eye. Starting with the design for the Ideal narrow FOV eye, the cemented interface was broken
and the FOV was iteratively increased using Hammer optimization until a lens solution existed at
55 degrees HFOV. The field points were updates to still use 12 fields but now evenly spaced in
5 degree increments. Since the distortion was set to a stringent requirement, much of the merit
function was able to be reused.
One challenge from preliminary work was the observation of the ray angles incident on the
image plane. This is an issue because an aim area or aim cone is required to define the
backwards ray trace. One test solution had ray angles exceeding 60 degrees AOI on the image
plane. Ray tracing required more than 250 attempts per ray (or 0.4% efficiency) for their cone or
aim area considerations. By restricting the cone angle, it was determined that significant
improvement could be found. This was necessary because a large diameter element near the
focal plane acted like a field flattener for many solutions. Thus, this was a necessity based on the
requirement of using a flat image plane. Setting the maximum ray angle on the detector to less
than 11 degrees seemed to meet the balance of ray tracing performance and sequential design
performance. An additional diameter constraint was added to the image plane such that it was
<55mm wide. This allows two eye models to be placed side-by-side for evaluation of small
IPDs. As an additional goal of optimization, it is desired to have excellent performance at
0.00E+00
2.00E-04
4.00E-04
6.00E-04
8.00E-04
1.00E-03
3 4 5 6 7
MF
valu
e
# of elements
Narrow FOV Merit Function
15 Deg HFOV - Real Glasses 15 Deg HFOV - Numerical Glasses
30 Deg HFOV - Real Glasses 30 Deg HFOV - Numerical Glasses
Page 44 of 57
narrow FOVs as well. In this manner the same wide angle lens can be used to gain high
resolution information by restricting the size of the detector appropriately. It is then convenient
to not have to switch eye models for the two types of analysis.
Starting with the 5 element system without doublets, the system was Hammer optimized using
automatic settings. It was then run in Global optimization mode for at least 2500 cycles. After
each run, an additional element was added in airspaces as a low power meniscus or flat. The
system was then reoptimized and this was performed iteratively until an 11 element system was
created. The merit function of each final solution was plotted in Figure 47. The goal was to
have a minimum number of elements to improve ray trace time and minimize input error. The
11 element solution looked best and was ultimately selected for input into LightTools.
Figure 47. Plot of wide Ideal lens merit function by number of elements.
In each spot diagram, the chief ray was used as the reference and the Airy disc was centered on
that location. The first system to have all geometrical rays within the Airy disc was the 10
element system. There was still marked improvement in the system going to 11 elements, so that
was selected as the final system. A 12 element system could have been tried to analyze the merit
function performance but was decided against due to computation time for the large number of
variables and the 11 element system already meeting the performance metrics. The performance
of this system matches the requirements and results set forth in Table 11. The prescription for
the 11 element solution is shown in Table 13.
0.0E+00
5.0E-04
1.0E-03
1.5E-03
2.0E-03
2.5E-03
3.0E-03
3.5E-03
4.0E-03
4.5E-03
4 5 6 7 8 9 10 11 12
Mer
it F
un
ctio
n V
alu
e
Number of Elements
Merit Function Values for Optimized 55 degree HFOV Lens
Page 45 of 57
Table 13. Prescription for Ideal Wide FOV Eye Model. All units in mm.
Surface Radius Thickness Index Semi Diameter
0 - Object Infinity Infinity 0.000
1 - Stop Infinity 0.012486 2.000
2 25.484636 3.110460 1.0998070 2.147
3 -3.259906 0.097488 3.069
4 -3.508120 0.345565 1.7340500 3.216
5 -4.114163 0.221424 3.620
6 -11.658705 0.061959 1.1918830 5.020
7 -210.347452 1.126908 6.110
8 -86.801440 0.131001 8.0777250 7.430
9 -69.461866 2.196302 7.439
10 -12.567586 0.505727 3.9153580 7.526
11 -11.153354 0.467530 7.566
12 -24.567679 0.155856 13.6465270 8.485
13 -23.340381 1.719599 8.508
14 -14.593251 0.084513 4.1279930 8.606
15 -16.324492 1.194084 8.793
16 -55.375366 0.319021 1.5236660 9.980
17 111.651331 6.564033 10.551
18 -75.311038 1.356898 3.2364220 13.618
19 -38.301755 5.768550 13.644
20 -15.450047 0.052458 5.2799610 13.653
21 -18.178830 0.051697 14.704
22 -431.615084 0.331581 42.8068350 23.103
23 -304.745794 0.944040 23.108
24 - Image Infinity 0.000000 22.843
The prescription shows several elements that are well beyond the typical index of refraction
values. Many of the lenses have poor thickness to diameter aspect ratios that are required in a
conventional design. Out of concern for precision in LightTools, values are shown and were
input into LightTools with 6 decimal places of accuracy. The Zemax lens layout and
performance are shown in Figure 48 and Figure 49, respectively.
Page 46 of 57
Figure 48. Layout for Ideal Wide FOV Eye Model.
a) b)
c) d) Figure 49. a) Spot diagram for Ideal Wide FOV Eye Model at 0 through 55 degree fields in
increments of 5 degrees. Scale is 40 microns. b) Diffraction MTF for Ideal Wide FOV Eye Model.
c) Field curvature and distortion plots for Ideal Wide FOV Eye Model. Scale for field curvature is
±0.100mm and scale for distortion is ±0.01%. d) Relative illumination plot for Ideal Wide FOV
Eye Model.
A general rule in any optical system is to minimize the number of elements. The use of 11
elements would be challenging if this were a physical system. However, since this lens will
Page 47 of 57
remain analytical, it only takes care to initially add the system into LightTools. Synopsys offers
a direct link between CodeV and LightTools that would minimize this work if the lens was
designed in CodeV. Since the work here was done in Zemax, manual entry will have to be
performed.
In this case, going to 11 elements is necessary to meet the desired level of performance defined
earlier. To meet the non-sequential raytracing requirements, the maximum angle of incidence on
the image plane is 11 degrees. The relative illumination shows significant change and will
require an adjustment of source power if comparing between the Narrow and Wide Ideal Eye
Models. The corrector “coating” is shown Figure 50 for this lens.
Figure 50. Angular dependence for the relative illumination corrector coating for the Ideal wide
field eye. Corrector coating is equal for all wavelengths (no spectral dependence).
One goal was to be able to switch to a narrow FOV and still maintain the required performance
parameters. The fields were reduced to match the previous analysis on the narrow field Ideal
eye. The geometrical spot sizes are shown in Figure 51. While the spot sizes have increased, the
maximum geometrical diameter is less than 1.72 microns for both lenses over 15 degrees HFOV.
This value is smaller than the mean spacing of the retinal receptors at 2.5 microns.
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
0 5 10 15 20 25 30 35 40 45 50 55
Tran
smit
tan
ce
Field Angle (deg)
Relative Illumination Corrector - Wide Ideal Eye
Page 48 of 57
a) b) Figure 51. Comparison of geometric spot sizes for a) narrow FOV and b) wide FOV Ideal lenses
for 0, 3, 6, 9, 12, and 15 degrees field angle. Scale bar is 10 microns for each.
The Wide Ideal Eye was then entered into LightTools using the QuickLens function. All radii,
thicknesses and indices of refraction were entered with six decimal places of precision. The
semi-diameters were fixed to not allow vingetting over the 55 degree HFOV. Lens materials
were set as non-dispersive and non-absorbing. Additional mechanical structure was added to
shield the detector from stray light coming from outside the eye.
Before adding to the system model, the relative illumination corrector performance was tested
using a Lambertian source at 550nm in front of the lens. Source power was 1 W over the entire
sphere, placed 0.1mm from the lens aperture, and oversized to 8mm circular diameter to fully
illuminate the lens. Figure 52 shows the performance of the lens with and without the relative
illumination corrector coating in place. As expected, the illuminance at the retinal plane is
constant across the field. With this lens now flat fielded, it can be used to compare the
performance of a simulated scene without introducing error that is significant to the simulation.
a) b)
Figure 52. Illuminance mesh of wide Ideal eye a) without and b) with relative illumination
corrector coating. Source power is the same for both measurements. Maximum scale is 315 lux for
both plots.
Page 49 of 57
Using the baseline model with no stray light, the wide Ideal eyes were placed in the model with
the stops at the appropriate eye relief of 10mm from the rear vertex. The system illustration is
shown in Figure 53 and shows the capability to place two eye models side-by-side.
Figure 53. Complete system in LightTools with Wide Ideal Eye Model.
The system model had no scattering or Fresnel reflection/loss on the components, which loaded
the same checkerboard and mask settings as previously used in the Arizona Eye Model
simulation. Using a backwards ray trace with a half cone angle of 11 degrees, a backwards ray
trace was performed. This ray trace took about 8 hours on a laptop, tracing a maximum of 2.147
billion rays. The receiver was set to 401x401 pixels and did not include smoothing, which
resulted in 1.98% error. Figure 54 and Figure 55 show the meshes for illuminance and color.
The power was not adjusted from the source to compensate for the decrease in on-axis
transmittance due to the relative illumination corrector.
a) b) Figure 54. On axis illuminance meshes for a) Arizona Eye Model and b) wide Ideal Eye Model.
Scales are set to the respective maximum for each plot and a minimum of 0 nits.
Page 50 of 57
a) b) Figure 55. On axis CIE meshes for a) Arizona Eye Model and b) Wide Ideal Eye Model.
The Wide Ideal Eye Model shows several advantages compared to the Arizona Eye Model. The
chromatic aberration of the lens is visibly apparent in the ideal eye, whereas it appears to cancel
out for this complete system using the Arizona eye. The distortion is also clearly apparent and
makes a good comparison to the stitched images of the narrow field eye. An advantage of
restricting the ray cone is that a plot similar to Figure 43 can be created by simply changing the
area of the retinal plane and maintaining the same aim configuration. For the wide Ideal eye, the
lack of distortion or chromatic aberration correction on the display is clearly apparent and could
be evaluated with the proper correction. Additionally, plots of proper color and relative
illumination performance, similar to Figure 44 could be generated in one step by performing a
ray trace with a fully white screen.
With the model performance tested, the stray light simulations were run using the same
parameters as the stray light analysis performed with the Arizona Eye Model. The same five
cases were run for comparison using the same ray behavior, counting the reference image shown
in Figure 55. Figure 56 shows the other four cases for the wide Ideal eye.
Page 51 of 57
a) b)
c) d) Figure 56. Illuminance meshes for stray light analysis using the Wide FOV Ideal Eye Model. All
meshes include Frensel transmittance/reflectance on the viewing lens with probabilistic ray
splitting. a) Fresnel on lens only. b) Black specular retaining ring surface added. c) Black
Lambertian scatter on mechanical housing. d) Black specular retaining ring and black Lambertian
scatter on housing combined. All charts set to a maximum luminance of 1.62 lux and a minimum of
1.62x10-4 lux.
The overall results produce the same conclusions previously seen with the Arizona Eye Model.
One of the advantages to the Wide Ideal Eye Model is that the angular extent of the stray light
can be observed better than the Arizona Eye Model.
With the final set of LightTools files completed, both forward and backwards ray tracing
performance can be analyzed. After performing a forward ray trace, LightTools has an option to
automatically calculate the aim parameters for the backwards ray trace. This method will be
compared with using a specified cone angle and setting the aim area to the clear aperture of the
last element. For the case of the specified cone angle, the ray angle on the image plane was
analyzed in Zemax to determine the maximum angle on the retinal plane. These half cone angles
were determined to be 35.17, 41.03 and 11.01 degrees for the Narrow FOV Ideal Eye, Arizona
Eye Model, and the Wide Ideal Eye Model respectively. As a comparison, a forward ray traces
from the display to the retina were run as well setting the Lambertian emitting cone angle to be
Page 52 of 57
15, 55 and 90 degrees. Backwards ray trace efficiency was defined by the number of rays
making it to the source as a percentage of attempted rays. Similarly, forwards ray trace
efficiency was defined as the number of rays reaching the retinal detector plane as a percentage
of attempted source rays. The simulation results are shown in Table 14.
Table 14. Ray trace efficiency for the various system eye models with no checkerboard on the
display plane.
Backwards Raytracing Efficiency Forward Raytracing Efficiency
Aim Area
Type
Cone
Angle
Aim
LightTools
Automatic
Solve
Aim Area
at Last
Element
Lambertian
Cone Half
Angle = 90°
Lambertian
Cone Half
Angle = 55°
Lambertian
Cone Half
Angle = 15°
Narrow Ideal
(15° HFOV)
4.21% 39.37% 1.24% 0.003% 0.006% 0.083%
Arizona Eye
(55° HFOV)
1.21% 41.15% 11.19% 0.111% 0.259% 1.666%
Wide Ideal
(55° HFOV)
11.09% 0.79% 0.40% 0.078% 0.183% 1.415%
Backwards ray tracing for this situation proved to be substantially more effective than forwards
ray tracing in all cases. LightTools made the best calculations when looking at the narrow Ideal
and the Arizona Eye Model. It did not have good performance for the wide Ideal eye, where
setting the cone angle provided the best performance. This may have been due to better
concentration of rays based on the geometries of the Narrow FOV Ideal Eye or the Arizona Eye
Model. Such a concentration may not be possible when meeting the distortion criteria or other
requirements set up for analysis. Thus, there will be more ray tracing time to obtain the desired
results from the wide Ideal eye.
Commentary and Additional Recommendations
The objective of this work was to create a complete illumination model of a commercially
available mobile virtual reality HMD exclusively by measurements of physical hardware. In this
process, work in both sequential and non-sequential lens design was performed. By designing a
viewing lens, creating CAD geometry, measuring source performance, creating a proper source
model, and evaluating different eye models, the foundation was set to analyze complete system
performance for color, relative illumination and stray light.
For this particular model, the display type and source were critical. Visual observations of the
display showed minimal color shift over viewing angle, which matched the chromaticity
measurements. Thus the variations of the emitted spectrum over viewing angle were not
expected. Combining the performance of the display with the transmittance of the PMMA optics
improved the chromaticity performance over viewing angle. Use of LCD over AMOLED would
have significantly increased the complexity of the model and likely caused more contrast and
viewing angle issues.
Stray light performance behaved as expected. The Fresnel reflection contributions at the center
of the field were limited to the central viewing angles of the system. This is likely due to
multiple interactions cause by the small angles of incidence near the optical axis of each lens.
Page 53 of 57
The textured nature of the housing made up for this and filled in the rest of the field. When
inspecting the Gear VR headset during mechanical measurements, the highly specular surface of
the lens retaining ring was of most concern for stray light contribution. This surface only
contributed stray light at the edge of the field, which was better than expected. This edge
contribution should still not be downplayed and can be improved in future designs. Another
recommendation for improvement is the use of AR coatings. A simulation using a quarter wave
of MgF2 designed at 550nm is shown in Figure 57 with the standard 4 orders of magnitude.
These significantly improve performance at the center of the field of view and eliminate some
stray light near the edge of the field. The contrast modulation improves to 99.8% from 98.5%
with the inclusion of this quarterwave AR coating. Improvements to the scattering of the plastic
mechanical features would also improve stray light performance.
a) b) Figure 57. Simulation a) without and b) with a quarter wave MgF2 coating designed at 550nm.
Scales are 1.61 to 1.61x10-4 lux and 1.76 to 1.76x10-4 lux for the plots, respectively.
One of the key tenants of VR is to have lifelike reproduction of real-life scenes. These scenes
should be free from aberrations when the reach the eye. Since these scenes are recreated using
optics, they will have aberrations, stray light, and other visual artifacts caused by the virtual
reality hardware. Thus, it is necessary to create a new class of tools that have no measurable
impact on the VR scene. For this report, it was the development of two “Ideal” eye models made
out of physical lens geometry – one narrow FOV and one wide FOV. The Narrow FOV Ideal
Eye enables higher resolution restricting the field of view while maintain the same number of
receiver bins. The wide field eye enables complete analysis of the field to determine various
contributions to stray light. The Wide FOV Ideal Eye Model has lower efficiency than the
Arizona Eye Model, but clearly shows the distortion and chromatic issues of the system.
One of the key assumptions for a new eye model for analysis was to use a flat image plane. The
use of a curved image plane, or more elements could restrict the cone angle and improve
performance. For these systems, the assumption is a 4mm stop as the first optical component of
the system. Based on first order properties, the increase of focal length of the lens would restrict
the cone angle on-axis based on numerical aperture. For the current lens at 16mm focal length,
the minimum cone angle becomes approximately 7.2 degrees. In order to meet the ray trace
Page 54 of 57
efficiency of the Arizona Eye Model, the focal length would require an increase to 25.4mm to
give some margin to create a 5.5 degree cone angle. Unfortunately, this would increase the size
of the eye model elements at a 55 degree HFOV to be oversized to not allow two eye models
side-by-side at nominal interpupillary distances. Thus, adapting the lens model to work at 21mm
focal length with a 4mm stop and a 6 degree cone angle seems most reasonable and efficient for
a redesign. An alternative would be to design a simple lens with a curved image plane and very
low distortion. This system could then be analyzed in LightTools to verify proper transformation
from the spherical detector to a flat detector plane. This would allow curvature of the image
plane as another variable for use.
Some of the unique challenges of illumination design and analysis for virtual reality systems
have been highlighted in this report. As this area and field are expected grow in the years to
come, the work here has been a good foundation for assessing other mobile virtual reality
systems as they arrive on the market. This work is also applicable to PC based virtual reality
systems as well.
Page 55 of 57
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