Artificial compound eye cameras are an attractive approach to generate imaging systems of maximum miniaturization. Their thickness can be reduced by a factor of two in comparison to miniaturized single aperture cameras with the same pixel size and resolution. The imaging performance of these systems can be improved significantly by the use of micro-optical refractive freeform arrays (RFFA). Due to the complexity of these non-symmetric surface profiles with sag heights larger than 50 µm in combination with extreme profile accuracies better than λ/14 (rms), there is no dedicated fabrication technology currently available. In the presented research, significant improvements in the fabrication of these elements with laser lithography were reached. Therefore, a laser lithographic process based on several coating steps in combination with a multiple exposure strategy was developed that is suitable for the fabrication of arbitrary freeform structures with sag heights up to 60 µm. In order to minimize surface deviations caused by unavoidable process nonlinearities, a compensation strategy based on an empirical process model is used. The achievable accuracy of the proposed method and its limitations were investigated by fabricating a spherical micro lens array for demonstration. The fabricated elements possess a shape deviation of less than 1.3 µm (rms) and can be used as master structures for a subsequent replication process in order to realize a cost efficient mass production of artificial compound eye optics on wafer level.
© 2012 OSA
Artificial compound eye cameras, as presented in Fig. 1 , are an attractive approach to generate imaging systems of maximum miniaturization [1,2]. Their thickness can be reduced by a factor of two in comparison to miniaturized single aperture cameras with same pixel size and resolution. In these systems the optical imaging is realized through different microlens arrays. These arrays are currently fabricated by using state-of-the-art micro-optics technology like the reflow of photoresist or reactive ion etching on wafer level to ensure a cost effective mass production of these elements [3–6]. Reflow of photoresist leads to well predictable and smooth surface profiles. Unfortunately, the degree of freedom of producible surface profiles is limited to spherical, cylindrical and ellipsoidal lenses. The latter ones are used in current compound eyes which help to compensate for aberrations such as field curvature and astigmatism for oblige angles of incidence. However, for optimum imaging performance the use of arbitrary surface profiles is highly desired to increase the optical fill factor and image resolution at a lower f-number. Figure 1(b) shows a refractive freeform array (RFFA) consisting of a decentered cutoff of a surface having a non-rotational symmetric shape. The diameter of the single lenslets of a complete array is in the order of 400 µm with a sag height of at least 50 µm.
Due to this non-symmetric freeform surface profile, the fabrication of these elements by the well-established reflow technology  is not possible. Diamond machining is a powerful technology to fabricate almost arbitrary freeform surfaces . However, up to our knowledge the currently available tool geometries prevent the 100% fill factor desired by the application. An approach for the fabrication of non-symmetric freeform structures with maximum fill factor is greyscale lithography using HEBS glass masks. This approach permits the fabrication of elements with sag heights up to 65 µm with a surface accuracy of 1% of the total structure height  which is not sufficient for the intended application. Therefore, the potential of laser lithography will be analyzed since it also allows for the fabrication of freeform arrays with maximum fill factor. This technology has been developed originally as a method for the fabrication of photo masks needed for photo lithographic structuring in the semiconductor industry . Furthermore, there is a huge field of application in the fabrication of micro- optics. Here, laser lithography is used for the fabrication of binary or multilevel diffractive optical elements, e.g. diffraction gratings and computer generated holograms even on non-planar substrates [11–13]. Specially adapted machines also allow the fabrication of elements with continuous surface profiles based on a grey scale lithographic process . Based on this concept, diffractive optical elements with continuous surface profiles or refractive freeform structures with sag heights up to a few microns can be produced with excellent surface accuracy [15–18]. Previous efforts to fabricate microlens arrays with large sag heights are based on single point laser writing systems [19,20]. These investigations could not reach the large sag height in combination with the needed surface accuracy for the application in high performance imaging systems. First investigations to fabricate refractive freeform arrays with a commercial fast scan laser writing system from Heidelberg Instruments  were limited in the achieved sag height. Outgassing effects of the photoresist during the exposure  could not be controlled in the case of sag heights larger than 25 µm which is not suitable for the intended imaging application. Furthermore, the compensation of process nonlinearities by merely adapting the grey scale table of the laser writing machine lead to a surface accuracy of 4 µm (peak to valley), which is not suitable for the application in a high performance artificial compound eye camera systems. In the following, we propose a laser lithographic process chain based on a multiple coating resist process in combination with a multiple exposure strategy to demonstrate the potential of a commercial laser lithography system for the fabrication of refractive freeform elements with sag heights up to 60 µm in combination with low surface deviations. In addition, an empirically based strategy for the compensation of fabrication imperfections due to nonlinearities in the lithographic process based on the adaption of the exposure data and their accuracy are proposed and discussed.
2. Fabrication technology
There are lots of publications reporting on the photolithographic fabrication of binary structures with extremely large sag heights up to some millimeters. These structures are applied in applications such as packaging, flip chip bonding and the fabrication of MEMS or reflow lenses [23,24]. Photoresists with a high contrast along with optimized process conditions have been developed to allow features like vertical sidewalls and large aspect ratios typical for such applications. In contrast to these demands, the fabrication of continuous surface profiles is based on the grey scale principle. A photoresist with low contrast is used to achieve a desired nearly linear correlation between the exposure dose and the obtained structure height in a subsequent development process. Efforts in order to optimize such ultra-thick lithographic processes, especially for the fabrication of continuous surface profiles are limited up to now to the photo lithographic fabrication based on grey scale photo masks [25,26].
2.1 Photoresist and exposure system
In our investigations, the commercial photoresist AZ 4562 (Microchemicals GmbH) was chosen because of its high viscosity in connection with its good grey scale performance. Three subsequent single spin coating steps were necessary to achieve a final resist thickness of 113 µm. Each spin step was done on a gyrset spin coater at a spin speed of 250 rev / min. Glass wafers with a diameter of 4 inch and a thickness of 2 mm were used as substrate. The baking of the photoresist, both, at the end and after each spin step was carried out on a hotplate. The laser lithography system FF 400 from Heidelberg Instruments was used for the exposure process allowing the modulation of the light intensity in 128 different intensity steps by an acousto-optic modulator. A second acousto-optic element deflects the laser beam into a 160 µm width exposure stripe which is scanned over the sample by moving the stage. The laser source of the system is a helium cadmium gas laser from Kimmon emitting at a wavelength of λ = 442 nm. At this wavelength, the photo resist possess a minor absorption compared to other exposure wavelength typically used in photo lithography (356 nm, 405 nm, 434 nm). In the subsequent development process, we used AZ 400K from Microchemicals diluted with deionized water in the ratio of 1:3 in a puddle development process.
2.2 Optimized process conditions
Nitrogen is a reaction product that inevitable occurs during the exposure of photoresists using a diazonophtonquinone (DNQ) based photo inhibitor. The amount of nitrogen created during the photo reaction is directly proportional to the amount of the degenerated photo inhibitor DNQ . This effect becomes extremely critical in the lithographic fabrication of micro structures with large sag heights. The technological challenge due to the necessity of a thick resist layer is caused by the deposition of the oblige exposure dose in the photoresist to achieve the desired structure height. The strategy to deposit the exposure dose has to prevent the generation of macroscopic nitrogen bubbles that might not leave the resist layer by a diffusion process. These macroscopic nitrogen bubbles result in profile errors or destroy completely the surface quality in the subsequent development process. Because the fabricated surface profiles shall be used in imaging applications, these effects have to be implicitly avoided in order to meet the required optical performance.
We used a test structure consisting of a blazed grating with a base of 800 µm to study the generation of nitrogen bubbles within the resist experimentally. After exposing and developing the structure, it was characterized with a white light interferometer (Micromap – Atos GmbH) after different development times. As shown in Fig. 2 , the nitrogen bubbles in the photo resist cause surface imperfections. Their surface topography was not resolved in the measurement and is represented in the measured height profiles as black spots. The size and density of these spots were used to evaluate the surface quality of the fabricated structures.
In order to deposit the oblige exposure dose, we used a multiple exposure process. The maximum dose deposited in a single exposure has been approximately 1200 mWs/cm2. According to the scan speed of the laser lithography system, the delay between two subsequent exposures was less than one minute. In addition, the baking process consisting of a temperature ramp with a final baking step had to be carefully adapted. The delicate relation between temperature and duration of the final baking step is presented in Fig. 2.
An increase in both, the duration and temperature of the final baking step, leads to a reduced photo reaction and though generation of nitrogen as a consequence of the reduced amount of photo inhibitor in the photoresist layer. At the same time, an increase in temperature and duration leads to a larger evaporation of solvent from the photo resist layer resulting in a higher viscosity and thus reduced diffusion speed of the generated nitrogen. An optimum is shown in Fig. 2(e) where almost no nitrogen bubbles were generated. As Fig. 3(a) shows for a fivefold exposure regime, the optimized baking conditions to prevent the formation of macroscopic nitrogen bubbles cause a minor loss of achievable structure height in comparison to non-optimized process conditions. Combined with a tenfold exposure regime, this permits the fabrication of microstructures with sag heights up to 60 µm without the occurrence of macroscopic nitrogen bubbles. The maximum achievable structure height depends nonlinearly on the number of exposures as shown in Fig. 3(b).
The fabricated thick resist layers show a strong nonlinear response to the deposited exposure dose as shown in Fig. 4(a) for a fivefold exposure regime. This effect in combination with the isotropy of the development process, schematically shown in Fig. 4(b), leads to strong profile deviations larger than can be accepted for the fabrication of micro-optical components for imaging applications. A method for the compensation of these nonlinearities in the exposure data is proposed in the next section.
3. Process simulation and compensation strategy
There are efforts to extend classical analytical photoresist models, e.g. Dill [27,28] for the simulation of continuous structures with large sag heights even in the field of micro-optics. The profile accuracy of the fabricated elements in these investigations has been limited to 1.5 - 2 µm [29,30] at a structure height of 100 µm which is not sufficient to some high performance imaging applications described in [1,2]. An alternative approach already used in mask based grey scale lithography is an empirical process description based on determining development rates experimentally [31,32]. As described by Hirai et.al. in , this approach has the advantage that there is no need for an additional experimental setup to determine the specific parameters of the analytical model which might be quite complex in the case of thick resist layers. To our knowledge, such methods have not been applied for the simulation and compensation of process imperfections of laser lithographic processes up to now. The applicability of such a method in the laser lithographic fabrication of structures with continuous surface profiles and large sag heights was investigated and is discussed in the following section.
3.1 Measuring development rates
We used a test structure shown in Fig. 5(a) to determine the development rate for each dose step of the overall 128 accessible dose steps experimentally. It consists of 13 single dose step areas with a size of 120x120 µm. After the exposure, the structure was developed for a certain development time. Consecutively, the height of each dose step was measured by using the white light interferometer. In subsequent steps, the structure was further developed for a certain time and characterized again.
By repeating the process of developing and characterizing the resulting step heights, the relation shown in Fig. 5(b) between structure height and total development time for each dose steps in the test structure was obtained. The test structure was placed on the wafer several times to avoid an influence by exposing during the measurement with the white light interferometer.
A cubic spline interpolation has been used to obtain the relation between structure height and development time for all 128 dose steps according to Fig. 6(a) . Finally, the development rate is given by the derivation of the structure height with respect to the development time for every dose step [see Fig. 6(b)], leading to a full description of the temporal development characteristics for each single dose value. With this information, it is possible to describe the development process for arbitrary surface profiles under the assumption that the structure is smooth and interactions between adjacent dose steps can be neglected. Figure 6(c) shows the development rate of a spherical lens without measures for process non-linearity compensation.
3.2 Time evolution of the resist surface
In Fig. 6(c) the absolute value of the development velocity, here denoted by the development rate is shown. The development velocity itself is a vector perpendicular to the surface to be developed instantly. In consequence, the direction depends on the local slope of the surface to be developed at any time in the process. A concept taking this effect into account is the string model [33,34]. The structure itself is sampled with a grid and the development process is sampled in N time steps. The local slope of the propagating surface has to be known at any time of the process in order to simulate the propagation of the surface during the development process. This information together with the previously determined absolute value of the development rate permits the calculation of the spatial displacement of each grid point.
3.3 Compensation of nonlinearities in the exposure data
Due to the concurrently influencing of both, the nonlinearities in the response of the photoresist and the isotropy of the development process inducing profile errors, a simple compensation by an appropriate adaption of the grey level calibration curve is not sufficient. As an approach to compensate these effects we propose an iterative algorithm as described in Fig. 7 . The design structure is split into 128 dose steps under the assumption that all dose steps show a linear behavior to get a first idea of the dose steps distribution to be exposed. On the basis of the previously determined empirical process model, the resulting surface profile is calculated. From the deviation between the designed and the simulated profile, a profile error and, hence the compensation is determined used to distort the design profile. The proposed algorithm creates a surface profile that is distorted compared to the design profile to compensate for the mentioned process nonlinearities. The algorithm has been implemented in 1D using the Matlab programming language.
3.4 Estimation of the limits of the compensation process
The accuracy of the proposed compensation approach is fundamentally limited by the accuracy of the input data for the calculation of the development rates as well as the reproducibility of the lithographic process. As can be seen from the white light interferometer measurement presented in Fig. 8(a) , the bottom of each dose step area is not totally smooth over the full area but shows a significant surface roughness.
Within each dose step area a region of interest (ROI) with a size of 40x40 µm2 was used in which a height value is obtained as arithmetic mean of all measured points within this window. The obtained value was then used as input data for the calculation of the development rates. The surface roughness of the dose step field is quantified by the root mean square value (rms) of the height distribution and represents the uncertainty of the determined steps heights. Experimentally obtained values for the roughness obtained with a tenfold exposure process are presented in Fig. 8(b) for 13 different dose steps at different development times. In average, the surface roughness (rms) is approximately 0.3% of the absolute structure height in case of a tenfold exposure process. The reasons leading to the described surface roughness are short term intensity variations within the laser scan during the exposure process. Figure 9(b) shows the intensity fluctuations of the 160 µm width laser scan used for exposure. The exposure intensity fluctuation during a single scan is in the order of 0.3% (rms) of the total intensity, but shows variations in the peak intensity up to 1.2%. They are caused by fluctuations in the emission of the gas laser itself in combination with the noise caused by the acousto-optical modulation of the laser beam.
The influence of this uncertainty of the input data caused by the roughness of the dose step areas on the accuracy of the simulated resist profiles was estimated using a single spherical lens with a sag height of 60 µm and a pitch of 400 µm as test structure. The uncertainty of the dose step measurement was quantified based on a statistical analysis. Randomly generated and normally distributed numbers were calculated within an interval with a width of twice the measured surface roughness, centered at the measured step height. These numbers were used to manipulate the measured dose step heights in order to simulate a statistical spread of the input data. Based on these input data the corresponding surface profiles in the photoresist have been simulated. The standard deviation of the constituent surface profiles has been calculated in order to quantify their spread to each other. The relation between the uncertainty in the dose step heights and the corresponding variation in the calculated profiles is shown in Fig. 9(a). Uncertainties of approximately 150 nm (rms) in the input data lead to an uncertainty in the calculated resist profiles of about 400 nm. This value represents an estimation of the lower limitation of the profile accuracy which can be reached by the proposed approach in combination with the used laser writing system. This limitation can be interpreted in terms of imaging quality using the Maréchal resolution criterion . It states that the image quality of an optical system can be considered as diffraction limited if the rms value of the wave front error is smaller than λ/14. In consequence, the surface deviation of a polymer lens with a refraction index of 1.5 has to be less than λ/7 which means less than 90 nm (rms) for a given wavelength of λ = 635 nm. As it can be seen from the previous consideration, the influence of the uncertainty of the dose step measurement on the accuracy of the simulated profiles of 400 nm is more than four times larger than the maximal permitted surface profile error by the Maréchal criterion to realize a diffraction limited optics. In conclusion, the proposed method can only be used for the fabrication of diffraction limited imaging optics, if the uncertainty of the input data can be reduced below 30 nm. This was only achieved with our laser writing system for sag heights up to 10 µm. In order to achieve this surface roughness for high sag structures, a further stabilization of the exposure intensity is needed. This might be realized by a stabilization of the laser source or by the implementation of a feedback control system to further reduce the surface roughness of the dose step areas.
Besides this fundamental limitation of the achievable accuracy of the simulated surface profiles given by the simulation approach, the experimentally achievable accuracy of the fabricated elements is further reduced by the reproducibility of the whole laser lithographic process chain. As discussed in Sec. 3, at first test structures have to be fabricated which are used to determine the development rates of the 128 dose steps needed as input data for the compensation algorithm. In order to achieve a high profile accuracy of the proposed method, the experimental conditions must not change between the processing of the test structures and the structures to be fabricated. This demands to ensure long term stability of the laser writing system as well as the environmental conditions like humidity and development temperature. The accuracy we could reach by using this approach with our laser writing system was investigated by fabricating a spherical lens array. The results are presented and discussed in the next section.
4. Fabrication of a spherical micro lens array with sag heights of 60 µm
4.1 Fabrication and characterization
In order to investigate the potential of the proposed method, an array of 25x25 spherical micro lenses has been fabricated. This lens shape allows, in contrast to the arbitrary aspheric surface profile of a RFFA micro lens array, a convenient and reliable characterization by a surface profilometer with high accuracy. It has to be pointed out that the process is not limited to spherical lens shapes, but allows the fabrication of arbitrary freeform geometries with continuous profile. The sag height of the single lenslets in the array was 60 µm with a pitch of 400 µm. These structures have been used for evaluation because their pitch and structure height represent typical requirements in the fabrication of micro-optical elements for imaging applications. According to Fig. 3(b), a tenfold exposure regime in combination with the optimized baking conditions described in Sec. 2.2 had to be used in order to achieve the desired structure height of 60 µm. A first sample was used to determine the empirical process model. Therefore, the number of dose step areas in the test structure described in Sec. 2 was extended from 13 to 32. Furthermore, the number of development steps was also increased to achieve a proper sampling of the process. This is mandatory to take effects like surface inhibition into account. Based on the obtained process model, a distorted surface profile was calculated compensating for process imperfections. Both, a compensated and an uncompensated surface profile, have been fabricated together with alignment structures to ensure a proper characterization using a surface profilometer (Talysurf – Talyor Hobson).
The fabricated micro lens arrays were characterized using a surface profilometer in order to quantify the profile error. Figure 10 shows the measured surface profile of the central lens of the array fabricated with compensated (solid blue line) and uncompensated (dashed blue line) exposure data in contrast to the desired lens shape (dotted blue line).
In addition, the profile error of the compensated profile (solid red line) and the uncompensated profile (dashed red line) from the ideal lens shape are plotted. Due to the compensation strategy, the profile error can be minimized from 6.8 µm (rms) to less than 1.3 µm (rms). The distortion of the compensated lens profile near the lens vertex is due to a non-sufficient number of dose step areas used to sample the process. Nevertheless, the achieved result according to structure height and surface accuracy is a significant improvement in comparison to previous efforts in the fabrication of RFFA by laser lithography. The improvement was achieved by a complex optimization of the resist and exposure process in combination with the proposed compensation approach. The achieved profile accuracy of 1,3 µm (rms) is slightly higher than the estimated theoretical limited of 400 nm discussed in section 3.4. This is caused by instabilities of the process conditions, e.g. temperature, humidity and long term fluctuations in the laser power. Improvements of the mentioned aspects are possible but require further investigation and optimizations.
There is a strong demand for micro-optical freeform elements intended for the use in micro-optical imaging applications. Elements are required with sag heights larger than 50 µm in combination with extremely low surface deviations. According to the complex surface geometry of the elements in combination with the large sag height and the demanding surface accuracy of the elements, there is currently no dedicated fabrication technology available.
The presented research shows the potential of a commercially available fast scan laser writing system for the fabrication of these elements using the commercial photoresist AZ4562. The outgassing behavior of the photoresist during exposure needed to be controlled carefully as it leads otherwise to macroscopic nitrogen bubbles and thus surface imperfections preventing the use of the fabricated elements in micro-optical applications. This was realized by developing a carefully adapted resist process, based on a multiple coating scheme. The fabrication of elements without surface artifacts caused by nitrogen bubbles and sag heights up to 60 µm was demonstrated using optimized process conditions. The developed process exhibits strong nonlinearities caused by the response of the photoresist in combination with the isotropy of the development process leading to significant surface deviations preventing the use in demanding micro-optical applications, such as imaging. An empirical process model in combination with an iterative compensation algorithm was used to compensate for these effects in the exposure data. The application of the proposed algorithm is currently limited to smooth surface profiles with feature sizes much larger than the diameter of the focus spot of the laser beam which is in the order of 1 µm. This is valid for the fabrication of micro lens arrays for imaging applications with lens diameters in the order of a few hundred microns. An extension of the empirical process model to non-continuous surface profiles is possible but requires further the modeling of the interaction between different dose steps in order to ensure sharp edges in the structures. The potential of the proposed approach was demonstrated by fabricating a micro lens array of 25x25 single lenslets with a sag height of 60 µm. The achieved profile error could be reduced significantly from 6.8 µm (rms) to less than 1.3 µm (rms) by using the proposed compensation method which demonstrates the huge potential of laser lithography for the fabrication of continuous surface profiles with sag heights up to 60 µm. The achieved result is a significant improvement in the laser lithographic fabrication of refractive freeform elements (RFFA) which were before limited to sag height up to 25 µm. However, the now achieved surface deviation of 1,3 µm (rms) at a structure height of 60 µm is nearly 15 times larger than the theoretical limit of 90 nm, given by the Maréchal resolution criterion for the fabrication of a diffraction-limited optical imaging system in the visible spectrum. In order to further improve the surface accuracy of the fabricated micro lenses, first the reproducibility of the whole lithographic process has to be increased to reach the theoretical limit of the compensation process. This limitation is given by the roughness of the dose step test areas used to generate the input data for the compensation algorithm. In case of our laser writing system, this limit was in the order of 400 nm due to a roughness of the dose step fields of about 150 nm (rms). In order to decrease this roughness, further measures like the stabilization of the exposure intensity e.g. by a feedback loop are mandatory. Much work needs to be done in future. Without these measures, the achievable profile accuracy does not permit the fabrication of diffraction limited high performance optical imaging elements but might be sufficient for beam shaping and illumination applications or for the fabrication of MEMS, MOEMS or microfluidic elements.
The work was founded by the Deutsche Forschungsgemeinschaft (DFG) within the priority program active micro-optics (SPP 1337). Furthermore, the authors would like to thank Mr. Marko Stumpf for his technical support and the maintenance of the laser writing system.
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