Prof. Jose Sasian

Diffractive Optical Elements

Lens Design OPTI 517

Prof. Jose Sasian

Diffractive Lenses

What they are

How they work

Zone spacing and blaze profile roles

First order properties

Dispersion

Two point construction model

Phase model

Sweatt

model

Efficiency

Diffractive landscape lens

Prof. Jose Sasian

Terminology

Diffractive optical element: generic term

Fresnel lens: Scale of zones and lack of organized phasing

Kinoform: Phased Fresnel lens. Phase modulation from surface relief

Holographic optical element: Produced by interfering two or more

beams

Binary optics: Made by staircases that approximate the ideal surface relief

Fresnel zone plate: A particular pattern that produces amplitude

modulation.

Hybrid lens: combined refractive and diffractive power

Computer generated hologram: A hologram produced by calculations in a computer

Prof. Jose Sasian

The work of a diffractive optical element

Organized rearrangement of the wavefront

Prof. Jose Sasian

Fresnel Lens

A Fresnel lens reduces the amount of bulk glass.Scale of zones is large and the wavefront segments are not rearranged to re-create

a spherical wavefront. The ring-zone segments is not properly organized.

mm

Prof. Jose Sasian

Two contexts for DOE: amplitude and phase

Blaze determines amplitude of diffracted ordersGeometry of zone boundary determines wavefront shape (phase)

The wavefront deformation introduced by a DOE is equal to thewavefront deformation represented by the DOE when it is thought

ofas an interferogram

Prof. Jose Sasian

Example

Straight fringes represent tilt and so the beam is deviated

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Example

Circular fringes represent defocus and so a DOE with these zone boundaries will introduce optical power

Depending on the spacing, spherical aberration can also be introduced

Prof. Jose Sasian

An infrared DOE

From Michael Morris

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A Fresnel lens cut-away

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First-order properties2 2

2 2 2 2 22n

n

f r f n

f r f nf n

f

2nr nf

r Given a focal length the zoneboundaries are defined.The optical path differenceBetween zones isone wavelength

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Paraxial diffractive lens definition

2nr nf

Prof. Jose Sasian

Zone Spacing

2

2 21 1 1

2

2 2

2 / #2

n

n n n n n n n

micrometersn

r nf

r r r r r r r dr ffSpacing dr Fr

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Focal length for a given spacing

0n construction construction

construction reconstruction reconstruction

r drf f

constructionDesigned for

Used at reconstruction

Prof. Jose Sasian

Prof. Jose Sasian

Diffractive V-number1

1 1f c f c

d d refractive

n n n nrn r n

/ 1 1/ 3.5

f c f c

d d diffractive

m dym d y

'sin ' sin mn nd

'y

1

sin ' /y yf

m d

Prof. Jose Sasian

Diffractive focal length from grating perspective

0

1sin ' /

/construction

construction reconstruction

construction

reconstruction

y yfm d

ym d

f

Prof. Jose Sasian

Modeling Diffractive Optics

Two point construction model

Phase function

Sweatt

model

Prof. Jose Sasian

Two point construction model

tionreconstruconconstructim ,,

tionreconstruconconstructim ,,

),,( ZYXA

tionreconstruconconstructim ,, ),,( ZYXB

Prof. Jose Sasian

Phase model

.....2 8642 dcba22 yx

Prof. Jose Sasian

Phase model

Prof. Jose Sasian

Sweatts

model 1n

For n~10,000 alpha must be very small to maintain The same deviation

1nr

For a plano convex lens with n~10,000The radius must be very long to maintainThe same optical power.

Prof. Jose Sasian

(1/d)

Prof. Jose Sasian

Sweatts

Model

(1/d)

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Dispersion in Sweatts

model

1

' 1

' '

1 10,0003.5

10,000 10,000

d

F C F C

d d drefractive

F C F C F C

n

Sin I Sin I n

Sin I Sin I n n

nn n

Prof. Jose Sasian

Dispersion in Sweatts

model

Schott: n()

= A+B +

'

' '

dd d

F CF C

d

drefractive

F C F C

mSin I Sin Id

Sin I Sin I md

md

md

Consistent with diffraction case

Prof. Jose Sasian

Structural coefficients: Thin lens (stop at lens)

DCYBXYAXySI 223441

2 212II

S y EX FY

2IIIS

2 1IVS n

0VS

12yCL

0TC

212

nnnA

22

1nnD

1

14

nnnB

11

nnnE

nnC 23

nnF 12

12

12

21

21

rrrr

cccc

X

uuuu

mmY

''

11

))(1( 1 xccncn

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Diffractive lens (n very large @ X=0)

23 1I Y 2II Y

1III

0IV

0V 1

Ldiffractive

0T C=3; D=1; F=2

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Aberration coefficients for Y=1; X=0

For general case one needs to be careful as the shape dependson the index for a given power.

22

20

IIyS f

2

0III

Sf

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Structural coefficients for diffractive lens

2

222

4 8 3 1IY YRR

2

2 2II YR

1III

0IV 0V

1L

diffractive

0T

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Field curvature correction hybrid lens

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Verification

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OPD Alternate view

OPD has two parts. One is due to material dispersion, the other to due to diffraction

2

2

2

2

2

1 12

1 12

1 12

12

1 12

FF F d

d

FF C F d

d

CC d

d

F CF C d

d

ref diff

yOPD n nR

yOPD OPD n nR

y n nR

y n n nR

y

OPD n t N

Prof. Jose Sasian

Spherical aberration

Depending on the zone boundary distribution DOE axially symmetric DOE can introduce different orders of spherical aberration

.....2 8642 dcba

Prof. Jose Sasian

Calculating order efficiency

Simple case of an amplitude device with a square wave profile

Duty cycle

0, **pxx y A Comb x nx rectd

m=0m=1m=2

Prof. Jose Sasian

Square wave

0

0 0 0 0

0 0 0

0 00

2

2 2 2 3 2 3

2 5 2 5 2 7 2 7

2 2 2 2

2 2

2 3

5 7

i n t

i n t i n t i n t i n t

i n t i n t i n t i n

A A nF SINC n SINC n

A nf t square wave SINC e

A A Ae e e e

A Ae e e e

0

10

...t

T

50% duty cycle

21 0.1

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Binary optics technology

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Efficiency for binary optics

Prof. Jose Sasian

Efficiency

2 2 1 212 2 22 3

11

2 222 2

22

1 1 1 11 1 12 2 3 3

11 2

1 4 1 113 4 12

113

2 ; 0.174 ; 0.7948 ; 0.94816 ; 0.987

hx h hn dx n x nN N N

hn h

hnN N

SN

N SN SN SN S

h/N

h

221S

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Efficiency

mnnc

onconstructi

tionreconstruc

tionreconstruc

onconstructi

11sin 2

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Efficiency222 21 1

3reconstruction construction

reconstruction

onconstructitionreconstruc

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Comparison Standard lens, Fresnel lens and DOE lens

Refracting lens Fresnel lens DOE lens

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Images of extended objects

Acrylic powerless lens

Other orders produce images at different magnificationsLike ghost images

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Canons multilayer DOEs

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How does it work?

Prof. Jose Sasian

How does it work?

2 1sin

1reconstructionconstruction

reconstruction construction

nc m

n

2 21sin sinreconstruction constructionreconstruction reconstruction

n dc d m c md

2 122 1

2 2 1 1

1 1sin

1 1

reconstruction reconstruction

reconstruction reconstruction

reconstruction reconstruction reconstruction

n nc d d m

or d n d n

Prof. Jose Sasian

100% at two wavelengths

Prof. Jose Sasian

Alternate view 100% efficiency at 2

(no ripple)

2 12 2 450nm

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An actual lens application for controlling chromatic change of magnification

Note lack of lens symmetry about the stop

DOE

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Plastic Fresnel lens; Diamond turned and replicated Gray scale; note binary edge

Binary 16 levelsBinary 8 levels

Some Fresnel lens and DOE photographs

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Measurement of a DOE

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Beware

Modeling assumes DOEs

having no physical structure

Real modeling faces sampling issues

Scal