We fabricated several long focal length microlens arrays with a fluid of index 1.60 ± 0.002. The standard array for testing was that of C5 which gives an overall focal length of about 4.7 mm and the microlenses are f/39 lenses. The testing of the hybrid microlenses are made on the Mach Zehnder interferometer.
(a) Quality of the microlens: point spread functions
The point spread function (Fig. 7.25a) of the hybrid lens on-axis is almost diffraction limited (Strehl ratio = 0.92). This is a significant improvement on the quality of the original microlens without index-matching fluid (Strehl ratio = 0.10). At 40° off-axis, the maximum angular position in the experimental configuration, there is an emergence of an asymmetric side lobe. However, the Strehl ratio is still acceptable (0.57), compared to 0.01 for the microlens without index matching fluid. The comparison is made between different microlenses in the array because of the difficulty in locating the same lens. However, the uniformity within the array is good and, therefore, the comparison is valid. The spot sizes of both foci are of the order of the diameter of the microlens and the microlens behaves rather like a light waveguide.
(a) (b)
Fig. 5.25 Point spread functions of the hybrid microlens (a) on-axis and (b) at 40° off-axis
(b) Angular dependence of astigmatism
We have also investigated the variation of astigmatism with the off-axis angle. The plot of astigmatism at various angles is shown in Fig. 7.26. If we now compare these results with those for a microlens without index-matching fluid, we can see that the long focal length hybrid microlenses are better at angles greater than 10°, otherwise they are comparable within the experimental error. The measurements for the hybrid lens cover only one off- axis side because we expect the results for the negative angles is very similar.
Microlenses: Design, fabrication and performances 180 e c cn 3 i
M icrolens with index-m atching fluid microlens without index-m atching fluid
-60 -40 -20 0 20 40 60
Angle of rotation, 0 0
Fig. 7.26 Comparison of the off-axis dependence of astigmatism between the microlens with and without index-matching fluid ((|) 120 |im)
We also made an array of f/13.7 microlenses from the array B4 with focal length of 3.28 mm. The astigmatic aberrations of these microlenses vary with the angle in a quadratic manner (Fig. 7.27). C5 microlens £^39 B4 microlens f/13.7
I
0.8 m s^
0.6 % 0.4I
.SP 0.2 < Angle of rotation, 0 0Fig. 7.27 Comparison of the off-axis dependence of astigmatism between hybrid microlenses made on (a) C5 microlens (f/39) (b) B4 microlens (f/13.7)
(c) Dependence of aberrations on focal length
The previous comparison between the hybrid microlenses from the C5 and B4 arrays suggest there is a dependence of astigmatism on focal length. Indeed, the astigmatism (in X) can be shown to be (Appendix HI) :
A = 8fk
where d - diameter of the microlens q - off-axis angle
f - focal length
(7.7)
Astigmatism is proportional to 1/f at a given angle, so the larger the focal length, the smaller the aberration. A plot of astigmatism against the focal length is shown in fig. 7.28a with the aberration normalised to that of the conventional microlenses. The worst case, at 40° off-axis, is taken and we find that the experimental result is in good agreement with the theoretical curve.
I - expt. result at 40' « 0.6 % 0.4 g 0.2 4.7 0.36 Focal length (f) [mm] (a) c o
I
0.8 I - expt. result at 0° S 0 .6I
^ 0.4I
I
0.2 4.7 0.36 Focal length (f) [mm] (b)Fig. 7.28 (a) Dependence of Astigmatism on focal length
(b) Dependence of spherical aberrations on focal length
In addition, we have measured the on-axis spherical aberrations (SA) of the lens and find that the large aberrations seen in the uncoated case (SA = 3.9 X) become
Microlenses: Design, fabrication and performances 182
negligible, i.e. within the experimental error of the measurement, for the longer focal length lenses. This is again expected as the SA coefficient varies as 1/f^ (Appendix IV) (Fig.
7.28b).
7.6.5 Imaging experiment using an apertured long focal length microlens
In our correlator system, each long focal length microlens images the entire input plane to the output, resulting in overlapping of the images at the output but this cannot be easily observed. Therefore, an opaque chrome mask was made to conceal the entire microlens array except for one microlens. This microlens, which is shown in fig. 7.29a, has a diameter o f 240 |im and focal length of 1.1 mm (f/# = 4.6). The index-matching fluid of index 1.60 was applied and the microlens was enclosed with a cover glass. The resulting focal length is about 15.4 mm and the new f/# is 64. This long focal length microlens is shown in fig. 7.29b. This is the longest focal length microlenses that we made.
An experiment (fig. 7.30) was set up to investigate the imaging properties of this apertured long focal length microlens. The microlens was situated at 2 / = 3 cm away from the input plane on which is placed a resolution target. The CCD camera is placed at 3 cm
(a) (b)
Fig. 7.29 Photograph showing (a) an apertured photoresist microlens and (b) after the index matching fluid has been applied.
away from the microlens and so the system is set up in a unity magnification imaging configuration. The illumination is provided by a LED and a diffuser. Only part of the resolution target can be viewed because of the mismatch in size between the image of the resolution target and the CCD chip. The finest line that can be resolved is no. 31 on the image of the resolution target. This correspond to 62.5 |L im . The diffraction limited
resolution was calculated to be 51.7 p-m. This shows that an almost diffraction limited spot size can be obtained with long focal length microlenses illustrating their lack of aberrations when used in a symmetric imaging configuration.
R esolution fPenured taroet microlens Monitor CCD camera
/
LED 3 cm 3 cm DiffuserFig. 7.30 Experimental apparatus for an unity magnification imaging experiment
The microlens was then replaced by a single pinhole with the same. The image was dimmer than before but the resolution is the same (resolvable line is 31). This agrees well with the predictions of the theory in chapter 5. Therefore, we conclude that the efficiency of the system can be enhanced by using a long focal length microlens array.
7.7 Conclusions
We fabricated several arrays of photoresist microlenses by deposition of the resist, u-v lithography and reflow. The array designs are on a electron beam mask made by RAL. There are many factors which can affect the final quality of the microlenses. W e find that the microscope glass slide is a better substrate and the uniformity of the array can be best achieved by high spin speeds of the photoresist. However, this often results in a thin layer of photoresist which does not have enough surface tension to draw into a convex shape
Microlenses: D esign, fabrication and performances 184
when melted. Consequently, a sag appears in the centre of the lens. The effect of melting time and temperature has been investigated and we conclude that reflow at 200° C for 10 mins is the best condition. The melting environment is another factor in fabrication of good microlenses. Furthermore, only short focal length microlenses (f/1 - f/4) can be made.
We have also measured the optical quality and aberrations of the microlenses using a Mach Zehnder interferometer. We can conclude that the photoresist microlens has better optical qualities than the latter. This is due to the presence of the surface profile on the NSG microlenses caused by swelling. Our best photoresist microlenses have a Strehl ratio of 0.88. The off-axis astigmatic aberrations are also investigated and we make a good quadratic fit to the relationship between astigmatism and off-axis angle.
To obtain long focal length microlenses from conventional photoresist microlenses, a layer of index-matching fluid is enclosed on top of the array. The difference between the indices of the fluid and the photoresist gives an overall longer focal length. The smaller the difference, the longer the focal length. We also have to determine the refractive index of the photoresist, which is found to be 1.64 ± 0.02 by focal length measurements. The quality of the long focal length microlenses is good in both on-axis and off-axis measurements. The point spread function is almost diffraction limited and the aberrations are minimal. These are expected in long focal length lenses as astigmatism and spherical aberrations vary with 1/f and 1/f^ respectively. The only drawbacks are that the spot size is approaching the size of the lens and the range of focal length becomes very long.