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Annals of the CIRP Vol. 56/1/2007 -545- doi:10.1016/j.cirp.2007.05.130
Geometrical Accuracy and Optical Performance of Injection Mouldedand Injection-compression Moulded Plastic Parts
W. Michaeli1; S. Heßner1; F. Klaiber1; J. Forster2
1Institute of Plastics Processing (IKV), RWTH Aachen, Germany 23M Deutschland GmbH, Neuss, Germany
Submitted by W. Eversheim (1), Aachen, Germany
Abstract The manufacturing of optical components by injection moulding and injection-compression moulding is a serious challenge for tool and machine technology as well as for process control. To evaluate the quality of optical parts the accuracy of the moulded geometry as well as the resulting optical performance has been analysed. At present a geometrical moulding accuracy in the lower micron range has been achieved for the production of thick-walled lenses. Overall injection-compression moulded lenses showed a better optical performance than injection moulded lenses. To further improve the resulting geometrical quality, local material shrinkage can be compensated by precisely modifying the cavity contour.
Keywords:Design, Mould, Optical
1 INTRODUCTION Optical systems made of transparent polymers compete economically with glass optics. Technological advantages in polymer processing allow increasing substitution of glass optics. The great freedom of surface design, the integration of several functional parts, good mouldability, low material costs and low specific weight (low density) substantiate the substitution potential. Injection moulding and injection-compression moulding allow a comparatively cheap one-step-manufacturing of high precision optical polymer lenses. The surface geometry of the optical functional area influences the optical performance substantially as well as internal properties. Lens quality is also affected by process control. Within statistical moulding trials the optimal process parameters were determined for manufacturing lenses with best optical and geometrical properties.To further increase the lens quality a strategy was developed to compensate local geometrical errors. The surface will be polished to locally compensate different shrinkage [1-3].
2 MOULD TECHNOLOGY
2.1 Mould base The injection moulding and injection-compression moulding trials are carried out with a mould base that complies with several requirements. A fundamental requirement was the modularity for using different mould inserts.
1
2
1
2
Figure 1: Cross-section of the mould concept and principle of centring
Furthermore the compliance with the desired surface contour and quality is important to reach the optical function of the lens. The positioning of the mould inserts in the mould base is achieved with a cone-alignment. The mould base can be used for both injection moulding and injection-compression moulding. For injection-compression moulding it is necessary to seal the cavity, before the polymer is injected. In Figure 1 the principle of the mould base is drafted.In the moving mould-half a conical centering ring (1) is mounted with a spring supported and touches the opposite side (the fixed mould-half) while closing the mould base to align both mould-halves with respect to each other. Subsequently the spring supported sealing ring (2) contacts the fixed half and seals the cavity. In this position the mould is not closed completely and it is possible to mould polymer optics using both process techniques injection moulding and injection-compression moulding
2.2 Lens geometry The dimensions of the sample lens are shown in Figure 2. For process analyses the optical area with a diameter of 50 mm is examined. The plane-convex lens has a diameter of 80 mm and a minimum wall thickness of 8 mm. The convex side has a spherical radius of 150 mm leading to a maximum thickness of 10.9 mm in the centre of the lens. The gating system is connected at the side with a 15 mm thick bar.
62,5
15
80
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8
R150
62,5
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80
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R150
Figure 2: Examined part geometry
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3 MEASURING TECHNIQUE
3.1 Geometrical accuracy The surface geometry is determined by a chromatic sensor. This sensor is based on the chromatic aberration of optical lenses caused by the wave length depending refraction index and allows a non-contact measurement. The specimen is illuminated by focused white light. A passive optic with high chromatic aberration expands the difference between each focal point of different light colours (Figure 3). A certain wave length is focused on the surface. This wave length is reflected with the highest intensity. This wave length can be correlated with the distance from the sensor to the specimen.
white light beam
Measurementrange 300 μm(or 3300 μm)
blue focal point
red focal point surface
white light beam
Measurementrange 300 μm(or 3300 μm)
blue focal point
red focal point surface
Figure 3: Measuring principle of the chromatic sensor
The surface contour of the mould inserts is determined as well. In an area of 60.5 mm x 60.5 mm 200 lines with each 200 measuring points are acquired. The test set-up has a measurement uncertainty of 2 μm. For analysing surface accuracy, the surface data were passed on to the evaluation program AIX-Comp, which was developed at IKV [4]. The three-dimensional surface data of the specimen and the mould insert are subtracted and the peak-to-valley-value (PVgeo) has been calculated. With this program a characteristic value for the maximum difference between mould and lens surface can be calculated for the plane and convex side of the lens.
3.2 Shack-Hartmann-Sensor The Shack-Hartmann-sensor (SHS) characterizes optical properties of lenses by simultaneously determination of the local wave front gradient at several positions. It is possible to reconstruct the shape of the wave front by mathematical integration. Further optical quality functions (PSF, MTF) and criterions (Strehl value, Zernike coefficients) can be evaluated by knowing the shape of wave front. A Shack-Hartmann-sensor is based on a lens array and a CCD chip [5]. The lens array subdivides the optical aperture into subapertures and images the tested light beam as focal points onto the CCD chip (Figure 4).
lens array focal plane(CCD-chip)
y
xdisplacement ofthe focal points
(x0,y0)
(x*,y*)dML
lens array focal plane(CCD-chip)
y
xdisplacement ofthe focal points
(x0,y0)
(x*,y*)dML
Figure 4: Principle of the Shack-Hartmann-sensor
Physically the SHS is based on measuring the displacement of the focal points. Out of the displacement
the local inclination of the wave front can be evaluated. The divergent light from a fibre-coupled laser diode (tested wave length = 635 nm) is collimated and imaged onto the SHS which determines the wave front aberration caused by the tested lens (Figure 5).
spherical wave front
aberratedwave front
Shack-Hartmann-Sensor
specimen Kepler telescopefibre-coupledlaser diode
spherical wave front
aberratedwave front
Shack-Hartmann-Sensor
specimen Kepler telescopefibre-coupledlaser diode
Figure 5: Set-up for Shack-Hartmann-aberrometry
Within the scope of the described examinations the measurements were accomplished by an existing test set-up at Optocraft GmbH, Erlangen. The wave front aberrations are specified in multiples of the tested wave length . The difference between maximum and minimum wave front aberration is indicated as peak-to-valley-value (PVWF) and used as a quality criterion to characterize the optical performance of the tested lenses. A further quality function is the point spread function (PSF), which can be calculated from the wave front. The function describes the luminous intensity distribution in the image plane of an ideal point which is imaged with a lens. With the PSF the Strehl value can be calculated, which is used as quality criterion for optical lenses, too. The Strehl value is the ratio of maximum luminous intensity in the image plane of a tested lens and the image of an ideal diffractively limited lens with the same aperture. With the PSF it is possible to calculate the modulation transfer function (MTF). To evaluate the resolution of a lens a critical contrast of Mcrit = 0.2 is defined. The spatial frequency which can be resolved with the critical contrast is a further quality criterion called critical frequency rcrit.
4 RESULTS OF INJECTION MOULDING AND INJECTION-COMPRESSION MOULDING TRIALS
4.1 Statistical evaluation The statistical evaluation shows that lenses with best quality are made with the following process parameters.
Injection moulding Injection velocity 20 cm³/s Cooling time 300 s Injection-compression moulding Embossing gap 5 mm Embossing velocity 3 mm/s Compression force 250 kN Cooling time 480 s
Table 1: Optimum process parameters
Geometrical accuracy The geometrical difference between mould and lens surface of injection moulded parts is close to the geometrical accuracy of injection-compression moulded ones (Figure 6). For the function of a lens in an optical system the geometrical accuracy but particularly its optical properties are of importance. The optical effect
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02468
101214161820
plane convex
IMICM
PV g
eo[μ
m]
02468
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plane convex
IMICM
PV g
eo[μ
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02468
101214161820
02468
101214161820
plane convex
IMICM
PV g
eo[μ
m]
Figure 6: Geometrical accuracy
results from the surface geometry and the internal properties of the lens. Contaminations of the polymer, molecular orientation or internal stresses can reduce the optical performance in spite of best geometrical accuracy.
Deformation of wave front To get reference values for the examined lens geometry the Shack-Hartmann-aberrometry was simulated by Optocraft GmbH, Erlangen, Germany. An optically ideal, aspherical lens would convert a spherical wave front, coming from the light source of the test set-up, into a totally plane wave front (Figure 7).
0.6
0 2010
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PVWF = 0.0
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PVWF = 0.6201
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x[mm]
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PVWF = 0.6201
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[ ] [ ]
Figure 7: Simulated deformation of the wave-front topography
The simulation of the test geometry causes a wave front deformation of PVWF, Sim = 0.6201 . This wave front aberration is systematical and is affected by the plane-convex test geometry. In Figure 8 the wave fronts of two specimens are displayed, each moulded with best process parameters.
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0 2010
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PVWF = 5.40014
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PVWF = 1.74236
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PVWF = 5.40014
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PVWF = 1.74236
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[ ] [ ]
Figure 8: Measured deformation of the wave-front topography
The aberrations of the injection-compression moulded lens are three times lower than that of the injection moulded lens, but approx. 2.7 times higher as the systematically deformation of the wave-front caused by the plane-convex test geometry.
Point spread function (PSF) Out of the wave front the point spread function can be calculated. For an optically ideal, aspherical lens a diffractively limited maximum of luminous intensity is calculated, which references the Strehl value.
1.0
0 0.06
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simulated aspheric lens
0.33 0.67
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v = 1.0
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v = 0.231
[-] [-]
Figure 9: Simulated point spread function
The image of the luminous intensity distribution of the simulated test part geometry shows a significant maximum in the centre (Figure 9). Around the centre there are concentric rings of secondary maxima caused by diffraction. The maximum intensity value is VSim = 0.231. In which way the wave-front aberration affects the imaging performance can be seen in the PSF of both specimens, each moulded with best process parameters. In Figure 10 the PSF of the best injection moulded and the best injection-compression moulded lens is displayed.
0 0.06
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0.060 0.015 0.03
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v = 0.0372
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injection moulding injection-compressionmoulding
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injection moulding injection-compressionmoulding
[-] [-]
Figure 10: Measured point spread function
It is evident that the ten times higher intensity in the centre results in a clearly better optical performance of the injection-compression moulded lens. In the PSF are only two concentric secondary maxima with lower intensity visible.
Modulation transfer function (MTF) The influence of lower optical performance on the contrast can be seen clearly in the MTF comparing lenses moulded by different moulding techniques.
Mod
ulat
ion
[-]
Spatial frequency [Lp/mm]0 50 100 150 200
0,00,10,20,30,40,50,60,70,80,91,0
diffraction limitsimulation
injection-compressionmoulding
injection moulding
Mod
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[-]
Spatial frequency [Lp/mm]0 50 100 150 2000 50 100 150 200
0,00,10,20,30,40,50,60,70,80,91,0
0,00,10,20,30,40,50,60,70,80,91,0
diffraction limitsimulation
injection-compressionmoulding
injection moulding
Figure 11: Modulation transfer function
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In Figure 11 the measured curves of MTF as well as the simulated curve of an ideally moulded lens as reference value and the physically maximum modulation of an ideally aspherical lens are displayed. The physically maximum modulation is limited by the diffraction and can not be reached due to the spherical geometry of the examined lenses. This is also shown by the simulation. The MTF of the injection-compression moulded lens follows close to the simulated curve and certifies a high accuracy by injection-compression moulding. In comparison to injection-compression moulding, the MTF of injection moulded lenses decreases clearly at low spatial frequency. In spite of similar boundary conditions (machine, mould, periphery) the optical performance of injection moulded lenses is clearly poorer than the optical performance of the injection-compression moulded lenses, which shows the advantages of the processing technology injection-compression moulding concerning achievable optical properties of polymer lenses [6].
5 LOCAL CORRECTION STRATEGY The moulding of a plane-convex lens is a challenge because the part thickness in radial direction is not constant. This results in a higher shrinkage potential in the centre of such lenses than on the outer edges.An improvement of the optical performance shall be reached through a compensation of the local shrinkage. Therefore the mould inserts will be corrected in the opposition direction of the shrinkage, to hold out the arising shrinkage error. It is necessary to iteratively repeat the shown process chain until the correct geometry of the lens is achieved (Figure 12).
grindingpolishing
measuringinsert moulding measuring
lens
correction-polishing
measuringinsert moulding measuring
grindingpolishing
measuringinsert moulding measuring
lens
correction-polishing
measuringinsert moulding measuring
Figure 12: Process chain
First studies conducted on the plane side of the lens showed, that the mould insert had a concave geometrical deviation of 5.2 μm due to the grinding process. The plane side of the moulded lens showed also a concave geometrical deviation of 4.5 μm, which has to be corrected (Figure 13).
insert
5.2 μm4.5 μm
lens
?
convex lens side
plane insert with concave deviation
plane lens side with concave
deviation
corrected insert surface geometry
insert
5.2 μm4.5 μm
lens
?
convex lens side
plane insert with concave deviation
plane lens side with concave
deviation
corrected insert surface geometry
Figure 13: Difference between mould and lens surface
To compensate for this deviation, the concave geometry of the plane mould insert was enlarged by local correction polishing [7, 8] to approx. 12.5 μm. The following characterisation of the moulded lenses showed that the mean deviation of the plane lens side could be reduced to 3.7 μm.
6 CONCLUSIONS Injection moulding and injection-compression moulding are primary forming techniques, which have a significant potential to produce optical parts in mass production. Especially in the area of imaging optics the requirements on the geometrical accuracy and on the optical performance are high. Very good process knowledge is a prerequisite to achieve and meet the required tolerances. Injection moulding offers the possibility to produce high precision parts with tolerances in the micron range. If the achieved precision needs to be further improved the injection-compression moulding technique and an appropriate mould can further increase the geometrical accuracy as the comparative studies have shown. Injection-compression moulded lenses showed much better optical properties than injection moulded lenses. For the production of polymer optics with high requirements on the optical performance the injection-compression technique has to be preferred. A further improvement of the quality of polymer optics can be achieved by local shrinkage compensation in the mould. This technique has been used successfully to improve the geometrical moulding accuracy of a plane surface of a plane-convex lens. In future studies the mouldability of free-form geometries shall be investigated in order to compensate the local shrinkage. Process knowledge will be gained and used in the future to predict the necessary local mould insert correction to achieve the desired lens geometry.
7 ACKNOWLEDGMENTS The support of the Deutsche Forschungsgemeinschaft (DFG) through the SFB/TR4 is gratefully acknowledged.
8 REFERENCES [1] Liu, X. D., Lee, L. C., Fang, F. Z., Lau, S. K.,
Chan, P. S., 2001, Shrinkage error compensation of plastic lenses by mold insert using diamond turning, Proceedings of the 2nd euspen Conference in Turin, Vol. 2: 698-701.
[2] Schmitt, R., Doerner, D., 2006, Measurement Technology for the Machine-Integrated Determiation of Form Deviations in Optical Surfaces, Annals of the CIRP, 55/1:559-562
[3] Brecher, C., Lange, S., Merz, M., Niehaus, F., Wenzel, C., Winterschladen, M., NURBS Based Ultra-Precicion Free-Form Machinig, Annals of the CIRP, 55/1:547-550
[4] Gärtner, R., 2005, Analyse der Prozesskette zur Herstellung mikrostrukturierter Bauteile durch Spritzgießen. Dissertation RWTH Aachen, Carl Hanser Verlag.
[5] Ares, J., Mancebo, T., Bara, S., 2000, Position and displacement sensing with Shack-Hartmann wave-front sensors, Applied Optics Vol. 39/10:1511-1520.
[6] Forster, J., 2006, Vergleich der optischen Leistungsfähigkeit spritzgegossener und spritzgeprägter Kunststofflinsen, Dissertation, RWTH Aachen, Carl Hanser Verlag.
[7] Brecher, C., Wenzel, C., Lange, S., 2006, Kinematic Influences on the Formation of the Footprint During Local Polishing of steel, Production Engineering XIII/1:23-26.
[8] Weck, M., Wenzel, C., 2004, Adaptive five Axis Polishing Machine Head, Production Engineering in XI/1:95-98.
