Fabrication of gray-scale masks and diffractive optical elements with LDW-glass

Transcription

1 Fabrication of gray-scale masks and diffractive optical elements with LDW-glass Victor Korolkov a, Anatoly Malyshev a, Alexander Poleshchuk a, Vadim Cherkashin a Hans J. Tiziani **b, Christof Pruß b, Thomas Schoder b, Johann Westhauser b C. Wu ***c a Institute of Automation and Electrometry, SB RAS, 639, Novosibirsk-9, Russia. b Institut für Technische Optik, Universität Stuttgart, 7569 Stuttgart, Germany c Canyon Materials Inc., San Diego, CA 9, USA ABSTRACT In the last years the application of gray-scale masks (GSM) for diffractive optics manufacturing attracts attention because of cost-effective possibility to produce a lot of diffractive elements on hard and heat-resistant thermally stable substrates. Direct laser writing of GSMs and fabrication of diffractive optical elements are effectively realized with application of LDW-glass (material for Laser Direct Write from CANYON MATERIALS, Inc). An important advantage of this material is the real-time change of transmittance in a single-step process without liquid development. It is shown that optimal transmittance range in which track width is not more than µm is from 5-% (transmittance of unexposed area) to 6-65% for LDW-glass type I having thinner colored layer. Power modulation and surroundings dependent peculiarities of direct laser writing on LDW-glass are discussed. Results of fabrication of diffractive optical elements using LDW-glass masks are presented. Among several types of LDW glasses studied the advantages of new GS- glass are elaborated. Application of GS- glass for GSMs allowed to fabricate blazed diffractive structures with backward slope width of.8 µm. KEY WORDS diffractive optics, LDW-glass, gray-scale mask, direct laser writing.. INTRODUCTION Applications of diffractive optics in hard conditions (high laser beam intensity or large variation of the temperatures, humidity) at long duration requires the development of a simple and cheap fabrication method for the continuous phase profile with high spatial resolution on the surface of optical materials with high mechanical and chemical durability, cold- and heat-resistance. The main candidate for this role is a gray-scale technology based on gray-scale masks (GSM) that change their transmittance (continuously or step-like according to a given function in a range, required for photolithographic process). Gray-scale technology permits using both contact printing without gap (unlike halftone method) and high-resolution projection lithography. The sequence of processes in gray-scale technology includes mask fabrication, mask printing to photoresist, photoresist processing, and transfer of profile from photoresist to the final substrate. The first step in this list is most innovative. Gray-scale microimage generation started from light writing on photoemulsion many years ago. Modern history of this problem began from 983, when high-energy beam sensitive glass (HEBS glass) was claimed as media sensitive to exposure by electron or ion beams, X-ray, and deep ultraviolet at wavelengths less than about -3 nm. The main exposure tool for this glass is certainly e-beam writing. In 988 direct laser writing of GSM on amorphous silicon films was demonstrated for the purpose of diffractive optics fabrication. In 99 direct laser writing on LDW-glass manufactured on the base of HEBS glass was patented 3. Multiple addressed deposition of metal film on substrate for gray-scale microimage fabrication with µm pixel size was published in This method requires N binary masks, poleshchuk.a.g@iae.nsk.su; fax ; ** tiziani@ito.uni-stuttgart.de; tel: 49-7/ ; fax: 49-7/ ; *** cwu@canyonmaterials.com; tel: ; fax: ; SPIE Vol. 444 / 73

2 N recurrences of photoresist processing and absorbing film deposition to get N levels of transmittance. Its application is limited by the accuracy of aligning the masks for different layers. LDW-glasses are manufactured from HEBS-glass 5,6 by flood e-beam processing of the surface. The e-beam processing results in a significant transmittance reduction of the surface layer. This darkening can be erased by heat at temperatures above about C. Local heating by focused laser beam with variable power is used to create the gray-scale image in the dark layer enriched by silver specs. Because high-energy electrons are mainly absorbed in depths of more than.5 µm the colored layer is formed beneath from glass surface (figure ). This considerably increases mechanical durability of GSM at contact printing since fine scratches don t damage the masking layer. However the presence of this gap and the large thickness of the colored layer result in dissipation of light and increasing backward slope of diffractive zones at contact printing. Figure. Schematic cross section of LDW-glass and impact of a focused laser beam on the heatsensitive colored layer. Depending on the conditions of surface preprocessing (ion exchange) and e-beam flood exposure the thickness of the colored layer can be varied from to 3 microns, and transmittance from to.% at UV spectrum range. At the present time several types of LDW-glass 7 are available: LDW-IR for writing in IR range (6 nm), LDW-HR for writing in visible range, and the newest type GS- (GRAY SCALE) glass almost achromatized in UV-VIS range. First two types of glasses have 3 sub-divisions depending on their optical density: type I (most transparent), type II, type III. We mainly investigated type I, because it permits to get a higher resolution than types II and III.. REQUIREMENTS TO INTENSITY OF LASER BEAM Transmittance, % nm 54 nm Beam power, mw % 46% 3% % Intensity, rel. units Figure. Exemplary characteristic curve (transmittance as function of beam intensity) for LDW-glass type I Scanning speed, cm/s Figure 3. Dependence of beam power on linear scanning speed at different given transmittance levels, 3, 46, and 6%. Material LDW-glass type I. The typical behavior of LDW-glass transmittance as function of the laser beam intensity (in relative units) is shown in figure. These curves were made for continuous writing mode when the power is not switched off between adjacent pixels. We used a focusing lens with N.A.=.65. Spot diameter was.8 µm. The dependence of the required beam power as function of the scanning speed can be evaluated from the plot on figure 3 for different transmittance (436 nm

3 wavelength) values. The dependence of power on scanning speed is practically linear in range from cm/s to 4 cm/s. However the behavior of the material considerably changes when scanning speed becomes less than cm/s. The required beam power decreases strongly nonlinear in this case. Pulse writing mode with generation of light pulses at positioning on a given grid requires higher beam power. The reduction of the pulse period increases the influence on the material because the heated region of the glass has no time to cool down between two consecutive pulses. As result the contribution of previous heating is increased, and less power is needed to get the same transmittance. It follows from the plot on figure 4, that heated volume of glass cools down in about -5 µs, as the influence of previous pulse is still evident after 7 µs. 7 Transmittance, % Figure 4. Dependence of transmittance on laser beam power at pulse writing: curve 9 µs pulse period, 37 µs, 3 8 µs, 4 7 µs. Pulse duration,4 µs. Beam diameter,8 µm. Distance between points of switching on of consecutive pulses.55 µm. Material LDW-glass type II. Wavelength 54 nm Laser beam power, mw 3. REQUIREMENTS TO FOCUSING LENS The requirements to the depth of field and focal plane of the focusing lens result from the thickness and the position of heat-sensitive layer. To characterize the colored layer experiments with liquid etching of the non-irradiated glasses were carried out. Figure 5 shows the kinetics of etching LDW-glass type I in a mix of 3 parts of 69 % HNO3, 8 parts of 5% HF and 4 parts of water. The measured values of optical transmittance (at 54 nm wavelength) are shown at the points of the etching depth. The etching depth was measured by profilometer DEKTAK-II. From this diagram it is evident, that the transparent top layer is etched more slowly than the colored layer. The cross point of the trend lines, which approximate the rate of etching for each layer, facilitates an estimation of the thickness of the top transparent layer as.35 µm from the point of view of chemical properties. The character of changing transmittance as function of depth of etching also corresponds to this estimation. The transmittance achieves 68 % at the depth of.9 µm. That is near the maximum transmittance achieved with laser writing (figure ). Thus, below a depth of about.9 µm the coloring specs disappear for a LDW-glass type I. It is evident that laser beam waist should be placed deep into glass. This conclusion is in good agreement with experimental results of laser writing at different focal plane (but with the same beam power). In figure 6, a focal plane on the surface is defined as shift. Negative values indicate, that the beam focus has been moved into the glass. Maximum transmittance is obtained, when the focusing lens is replaced about µm down from being focused on the glass surface. Plot of figure 6 was measured for LDW-glass type I. Thick colored layer restricts a minimal depth of field of the focusing lens because the usage of a short depth of field results only in heating the upper part of colored layer. In this case the lower part can be decolored only for account of thermal conductivity. But the thermal mechanism operates effectively only at low scanning speed. Therefore realization of high speed laser writing requires to use the depth of field not shorter than the thickness of colored layer. For a focusing lens with N.A=.65 we receive spot radius ω =.4 µm. The depth of field D can be estimated from equation of Gaussian beam propagation:

4 D = π ω ω λ ω where λ - wavelength (54 nm), ω - spot radius at edge of field. We consider edge of field at decreasing intensity in spot by %, that corresponds to ω/ω =.. Therefore, the depth of field is.9 µm. This value is even less than the thickness of colored layer for LDW glass type I. Thus, numerical aperture.65 is maximal for effective laser writing in a wide range of scanning speed. For LDW glass type II and III, having layer thickness of -3 µm, numerical aperture should be decreased at least to.45., Depth, microns % 8.3% 4.5% 4% 5 5 Etching time, sec Transmittance, % Defocus, micron Figure 5. Etching kinetics of unexposed LDW-glass type I. Straight line approximates rate of etching of upper transparent layer, and straight line approximates rate of etching of lower colored layer. Values near squares represent current transmittance of etched area. Figure 6. Transmittance (54 nm wavelength) of areas exposed at the same beam power but at different defocusing from surface. Shift of focusing lens in relation to position of focusing on surface.9 micron is optimal (focal plane is under surface of sample). Numerical aperture of focusing lens is.65. Wavelength 54 nm. 4. OPTIMAL TRANSMITANCE RANGE AND SPATIAL RESOLUTION The spatial resolution is one of the most important criteria for the recording layers. It generally depends on thickness and structure of the layer. The thickness of the modified colored layer of the LDW-glass should be not less than µm because of low concentration of silver specs. Nevertheless the low heat conductivity of glass and the localization of transmittance change around the top of light intensity distribution result in a rather high spatial resolution. The effect of localization is caused by a sharp reduction of light energy absorption after sufficient bleaching an area around the center of Gaussian intensity distribution. In practice of manufacturing GSMs, the width of the recorded tracks defines the minimal backward slopes (transition between minimum and maximum phase at the boundary of zones) of the diffractive zones and a choice of optimal overlapping the adjacent tracks. We investigated the dependence of track width on the transmittance at 436 nm wavelength for LDW-glass type I. This dependence in figure 7 shows that a rather high spatial resolution is achieved for transmittance below 6-65 %. It is also convenient to use the transmittance range up to 65 % because the curve is far enough from saturation and less beam power is required for writing (figure ). A sharp increase of track width at a transmittance higher than 6-65 % can be interpreted as follows. In LDW-glass type I, the concentration of silver specs increases from transparent surface layer to the center of colored layer and then decreases (figure ). The heat erase moves in depth direction and bleaches elementary layers one by one. The light energy absorption decreases, when the erase front reaches the elementary layers with low concentration of colored specs. Further the transmittance increases mainly due to thermal conductivity in underlying low-absorbing elementary layers. However, if the temperature front reaches a large depth it distributes approximately the same value in lateral direction. Thus, the heat erase on full depth results in a significant growth of the width of the decolored tracks.

5 .6 Track width, micron.4..8 Figure 7. Dependence of track width on transmittance (436 nm wavelength). Scanning speed of writing beam 7 cm/s. Material LDW-glass type I. Beam diameter.8 µm Transmittance, % Although the halfwidth of track can be made not more than.5 micron, the real backward slope of photoresist structures made by contact printing is much more. Figure 8 shows profile of diffractive zones made by contact printing of a grayscale mask made of LDW-glass type I. The backward slopes are.5 micron. It means that contact printing adds a considerable contribution to shape distortion. Figure 8. Profile of diffractive zones made by contact printing of GSM to SC87 photoresist. Material of GSM - LDW-glass type I. Ddepth, nm Coordinate, micron Figure 9. AFM profilogram of structure in photoresist, made by contact printing of GS- glass mask. Looking for a higher spatial resolution of GSMs we also investigated a new type of LDW-glass named GS-. The colored layer of this material is thinner than one of LDW-glass type I. Another distinctive attribute of GS- is its considerably achromatized characteristic curve (weak dependence of transmittance on wavelength of exposure

6 illumination) that gives some advantages in technological process. Experiments with contact printing of the test grayscale microstructures made in glass GS- have shown a substantial improvement of backward slope of profile in photoresist. The profilogram on figure 9 shows the shape of a backward slope of some diffractive structure in photoresist. The width of backward slope is equal to.78 microns (the region between two vertical lines). Thus, the application of these glasses permits a considerable improvement of the spatial resolution of gray-scale masks in comparing to regular LDW-glass. Another reserve for increasing the spatial resolution is the application of beam shaping. The size of a spot can be reduced approximately by 3 % for account of increasing side-lobes of light intensity 8. This technique uses threshold behavior of heat-sensitive material to cut influence of side-lobes. However it is not so obvious, that less track width will result in so essential reduction of backward slopes, as the contribution of the photolithographic process will not change. However beam shaping will allow to use LDW-glass with thicker colored layer (type II and type III) that will increase contrast of a GSM and accordingly will reduce the influence of lateral etching on the backward slope. 5. POWER MODULATION AND SURROUNDINGS DEPENDENT PECULIARITIES T X X P T Time Time (a) P (b) X Time T T X Time (c) (d) Figure. Bright (a and b) and dark (c and d) contouring : (a) and (c) depict the influence of track overlapping on transmittance distribution, (b) and (d) depict the influence of power modulation on transmittance distribution. T transmittance, P beam power, X coordinate across beam scan direction (arrow of X axis indicates direction of shift of scan trajectory). Action of laser beam on LDW-glasses is accompanied by return influence of changed transmittance on energy absorption in colored layer. It causes several features to be taken into account at fabrication of real GSMs. One of these features concerns overlapping of the area exposed by the focused laser beam and of the adjacent track exposed earlier. The interline spacing is recommended to be in a range of.5-.5 times the spot size in order to avoid gaps between the tracks. We usually used.3 µm interline spacing at a track width of up to µm. The surroundings formed before exposing the current track influences the achieved transmittance. The more overlapping, the stronger the influence because more energy can be lost falling into adjacent bleached track, and vice versa more energy can be absorbed falling into adjacent low-exposed track. However more overlapping decreases parasitic modulation of transmittance distribution. Too much energy or insufficient energy at the boundary of gray-scale zones give rise to two types of

7 contouring of gray-scale diffractive zone: bright and dark contouring. These phenomena are depicted in figure and figure. The bright contouring arises when exposing the gray scale zones with maximal transmittance at the starting zone boundary. The first pass of the beam with high power on zone border gives higher transmittance than next passes with the same power, because this first pass falls into high-absorbing area (figure a). Surface even melts on the first track. On the following tracks the field exposed by the beam falls partially into decolored previous track, and a significant part of the beam energy travels through the glass without being absorbed. Local melting of the glass surface on the zone borders results in the formation of surface ridges (figure, a). Surface ridges and transmittance peaks scatter actinic radiation during printing of GSM along the zone borders and sharply worsen backward slopes of phase diffractive zones. This problem is not solved completely even by increase of the maximal transmittance in gray-scale zones up to highest possible one, because melted ridges scatter light anyway. Bright contouring takes place when the power is modulated along the scanning trajectory (figure (b)). If exposure of gray-scale zones begins with minimal beam power then dark contouring can occur (figure, c, d). When the minimal transmittance in a gray-scale zone is chosen considerably higher than the transmittance of unexposed material the beam power on the pass following a pass with high power can be insufficient to get this minimal transmittance (figure (c), and similar case for power modulation (d)). This type of contouring is easily avoided by reduction of minimal transmittance in gray-scale zones to the transmittance value of the unexposed area. Still the surface relief with depth about 5-3 nm was observed (figure (b) and (c)). (a) (b) (c) Figure. Surface figure of GSM written at different trends of beam power: (a) - white light microinterferogram of GSM written with sharp changing beam power from min to max at boundary of diffractive zones (melted tracks are visible as peaks on fringes); (b) and (c) GSM written with sharp changing beam power from max to min at boundary of diffractive zones ((b) transmission microphotograph, (c) - white light microinterferogram of surface). The influence of the surrounding when writing a track is not limited by appearance near the borders of gray-scale zones. This is illustrated in figure. The processing with increasing a beam power from track to track gives higher value of transmittance (T up in figure ) than with decreasing (T down in figure ) the power at the same power level. In the case of increasing power, the beam falls partially into adjacent previous track which is darker. Therefore, a larger fraction of laser beam energy is absorbed. At the first glance, the difference between the curves is insignificant. Nevertheless, the plot of the ratio T up /T down as function of beam power reveals that within the first part (8-4 %) of the curve the ratio of transmittances is far from. It is easily explained by the higher ascending slope of the dependence T(P) on the initial part of the curve, so the sensitivity to the factors influencing the absorption of energy is maximal. Curves T up (P) and T down (P) on figure were measured by scanning photometry 9 of a gray-scale structure with µm width. It is very likely that the difference between these curves will increase with reducing a zone width because of larger power step between adjacent tracks. In an extreme case of jumping between only two power levels (maximum and minimum) contouring effect will be observed.

8 T, % Tup/Tdown Tup.6 Tdown P, rel. units Tup/Tdown Normalized depth.8.6 Hdown Hup.4 Ideal Normalized coordinate Figure. Transmittance T (wavelength 436 nm) as a function of beam power P at writing with increasing power (curve T up ) and decreasing power (curve T down ) from track to track. Figure 3. Normalized profile depth as function of normalized coordinate in diffractive zone for using GSM written with averaging characteristic curve T(P)=(T up (P)+T down (P))/. 6. METHODS FOR REDUCING OF WRITING ERRORS Gray-scale masks of DOE, in which the phase is constant along a trajectory of beam scanning, can be written rather easily without errors. For x-y systems such DOEs are cylindrical lenses, linear gratings, and their crossed twodimensional combinations. The class of similar elements for circular writers includes rotationally symmetric lenses, axicons, and aberration correctors. The approach to such DOEs is based on two factors. First, the invariance of beam power along a trajectory of scanning makes writing independent of the behavior of heat-sensitive material to beam power modulation. Secondly, the diffractive zones may have the same tilt direction, or two opposite directions (tilt for circular DOEs is defined along radius) and these zones can be separated into groups. As result, each type of inclination is written in direction of increasing beam power from track to track within the boundaries of each gray-scale zone. If the DOE has two types of zones, they are exposed in turn, one group after another. Undoubtedly writing in turn requires very good reproducibility of the scanning system. Thus, viable alternative of direction of scan trajectory shift ensures the correct characteristic curve and absence of contouring. GSMs with arbitrary topology require solving these problems in another way. The influence of the difference in characteristic curves can be minimized using an average characteristic curve (Tup(P)+Tdown(P))/. It is useful to estimate the resulting error for this case. Assume that GSM with transmittance range from 8% to 6% is printed to photoresist with linear response curve. Figure 3 shows the normalized profile depth H as function of normalized coordinate in diffractive zones with different inclination. Influence of profile shape error on diffraction efficiency can be estimated by the formula for linear gratings : H η = sinc, H where H maximum deviation of profile depth between ideal and distorted shapes. Note that the sign of curvature is unimportant. In the case described by figure 3, the value H/H is approximately equal to.4. Therefore, the maximal diffraction efficiency is 99.7% for continuous relief with ideal backward slope. The loss is negligible for most applications. But for the case of refractive microoptics and multi-order DOEs this error becomes more noticeable. For example for DOE operating in the 5th order the efficiency decreases to 9% for H/H =.4. Another problem to be solved at fabrication of arbitrary GSM is contouring caused by both effects: power modulation and surroundings (figure ). However in many cases, contouring because of surroundings doesn t influence noticeably the performance of GSM with arbitrary topology since it evidently appears if laser beam goes along zone boundary during long time. The effect with power modulation can be eliminated on a hardware level. It is necessary to

9 change the front shape at jump of power from minimum to maximum. The method, introduced in figure 4, is based on thermal integration of action of short light pulse and following switching off for the same short time. This method allows to receive a relative independence on a maximum level of power in gray-scale zone. The duration of transition process depends on scanning speed V of writing beam. This dependence can be evaluated as a crossing time by writing beam for distance equal to half of the width d of the recorded track: = d τ f. V Experiments have proven the applicability of the method, the contouring of diffraction zones was eliminated. The microphotograph of a segment of a GSM made in the light transmission microscope is shown in figure 5 (a). Figure 5 (b) shows white light reflection microinterferogram of the same segment of the GSM. Left and right sites (in relation to vertical line) were written with opposite gradient of beam power. Typical contouring peaks on interference fringes in figure (a) are absent in figure 5 (b). Power Figure 4. Front modification at beam power modulation. Time (a) (b) Figure 5. Elimination of the contouring : (a) microphotography (in transmission) of gray-scale mask written with modified front of light pulse; (b) microinterferogram of the same surface in white light. 7. PECULIARITIES OF PHOTOLITHOGRAPHIC PROCESS WITH GSM Gray-scale photolithographic process has some peculiarities as contrasted to binary process. At first, it is desirable to make preexposure of photoresist layer. This ensures operation in the linear part of the response curve of photoresist. It simplifies the adjustment of the fabrication process, increases the accuracy of relief formation (since the full range of transmittance variation is used), and also reduces the contribution of quantization noise of GSM to surface roughness. Secondly, the spectrum of actinic radiation influences the shape of surface relief, as transmittance distribution of the GSM differs on i, g, h lines. Therefore, if using custom-made GSM, it is desirable to use illumination with only one working line. In the present paper we give the main attention to peculiarities of heat erasure property of glass GS-, as insufficiently explored material and perspective. The dependence of transmission spectrum of this glass on writing beam power is shown in figure 6. From these plots it is visible that the transmittance at wavelengths 436 and 45 nm is practically identical at every beam power level. Therefore, GSM can be used for exposition on both lines or on their arbitrary combination. The behavior of transmittance at wavelength 365 nm essentially differs. Figure 7 depicts the dependencies of transmittance at wavelengths of actinic radiation on transmittance at wavelengths of writing beam (54

10 nm). These dependencies are used for conversion of transmittance distribution (T at 54 nm) measured by means of built in writer scanning photometer 8 to transmittance distribution at wavelength of exposure. Such method allows to avoid calibration of gray-scale photolithographic process with test gray-scale structure if the response curve of photoresist is well known or in the case of thin film photoresist. Transmittance, % Wavelength, nm Figure 6. Transmittance spectrum of GS- glass at different values of writing beam power ( 54, 39, 3 3, 4 6, 5 mw). Scanning speed 67 cm/s T at 365,45, 436 nm, % nm 365 nm nm T at 54 nm, % Figure 7. Interrelation of transmittances at wavelength of writing beam (54 nm in this case) and wavelength of actinic radiation (365, 45, or 436 nm) used for exposure. 5 µm (a) (b) Figure 8. Built-in test structures for check of transmittance function of GSM and profile shape: (a) - fragment of GSM with built-in test structure, (b) white light interferogram of the test structure in photoresist. The correctness of profile depth and shape is a particularly important issue in gray-scale technology. To define an uniformity and reproducibility of mask parameters and manufacturing process we build into GSM some test rectangular frames (figure 8 (a)) at various distances from center of GSM. The identical test patterns on every DOE and their independence on sizes of surrounding diffractive zones make the checking process considerably easier. Because of the small sizes (about x µm ) of such inserts the effect on diffraction efficiency of whole DOE is in general negligible. The exemplary interferogram of profile of test frame in photoresist is shown in figure 8 (b). 8. APPLICATION OF GRAY-SCALE MASKS FOR DOE FABRICATION For fabrication of GSMs we use the circular laser writing system CLWS-3, adapted for direct writing on LDWglass. This system is especially effective at writing of axial symmetric DOEs. For this class of elements the number of gray-scale levels can reach several hundreds at mask size of up to 5 mm (maximum for LDW-glass masks). Radial positioning accuracy is ±. micron. The accuracy of measuring an angular coordinate is ± sec. Moreover this system is also well suitable for fabrication of arbitrary gray-scale masks. Figure 9 (a) shows the grayscale mask we manufactured and used for fabrication of a diffractive slow axis collimating optic for laser diodes. The phase function of the element was defined using two-dimensional polynomials.

11 5 µm (a) (b) (c) (d) Figure 9. Application of LDW-glass for gray-scale fabrication: (a) gray-scale mask of DOE for slow axis collimating optic for laser diodes; (b) Fresnel lenses with diameter of and mm on fused silica substrates; (c) Fresnel lenses on silicon wafer (lens diameter 5 mm, N.A.=.58); (d) - gray-scale mask with diameter of 5 mm for fabrication of Fresnel lens on silicon wafer (reduction :). To evaluate the capabilities of gray-scale masks for manufacturing of high-performance DOEs we made an estimation of diffraction efficiency of Fresnel lenses which were fabricated by using GSMs from LDW-glass type I and LDWglass GS-. The diffraction efficiency of lenses at given backward slope was estimated by integration of the contribution of zones with different zone width. The efficiency of each zone was calculated by the formula for a linear grating. The profile of zones were considered as continuous and having an exact angle of inclination. The estimations were made for two types of illumination (Figure, and 3 - constant illumination;,4 - Gaussian beam) and two values of backward slope BS (BS=.5 micron - for and curves, BS=.8 micron - for 3, and 4 curves). The advantage of LDW glasses GS-, having backward slope of.8 microns, is apparent. In real practice we have obtained 85 % efficiency for lenses in photoresist (at profile depth optimized for refraction index of.6) and the average efficiency 8 % for lenses in fused silica (figure 9 (b)). For fabrication of these lenses we used GSMs on the LDW-glass type I. Minimum periods of zones was 8 microns. The measurement of diffraction efficiency was made at illumination similar to constant. The relief of diffractive lenses formed in photoresist was transferred to fused silica with ion-plasma etching. Working gas was CF 4. The etching was made in a RF system with grounded anode. The samples were placed on the electrode being under voltage. Besides DOEs on fused silica substrates we manufactured the lenses on silicon wafers lenses for far IR range with 4.4 mm focal length and 5 mm diameter (figure 9 (c)). The numerical aperture of these lenses was N.A. =.58. The lenses were produced by projection printing of gray-scale LDW-glass type I mask with diameter 5 mm (figure 9 (d)). The etching of silicon was made in gas mixture of SF 6 and oxygen.

12 Efficiency, % Min. zone width, micron N.A. 4 3 Figure. Estimation of diffractive efficiency of Fresnel lenses as function of numerical aperture for different types of illumination and backward slope (BS): and 3 constant illumination;,4 - Gaussian illumination;, - BS=.5 µm, 3,4 BS=.8 µm. Wavelength 633 nm. 9. CONCLUSION Laser direct writing on heat-sensitive LDW-glasses has shown excellent prospects for gray-scale mask fabrication. LDW-glass GS-, which allows to get.8 micron backward slope at contact printing, is particularly promising. Highperformance fabrication of GSMs requires to take into account a number of peculiarities of LDW-glass. Optimization of mask fabrication has shown that maximum spatial resolution is reached in transmittance range from 5-% (original value of unexposed material) to 6-65 % for LDW-glass type I. Diffraction efficiency of Fresnel lenses fabricated using contact printing of GS- glass masks can reach 8% at numerical aperture. for Gaussian illumination, and increases up to 9% when N.A. decreases to.. ACKNOWLEDGEMENT The authors would like to thank R. Dederer for help with preparation of several experimental samples and pictures for this paper. REFERENCES. C. Wu. High energy beam colored glasses exhibiting insensitivity to actinic radiation, US Patents No , January 8, 986 (filed on June 4, 983).. V.Z. Gotchiyaev, V.P. Korolkov, A.P. Sokolov, Optical recording on amorphous silicon films: optical and structural changes, spatial resolution, Proceedings III Intern. Symposium on Modern Optics, II, pp , Budapest, C. Wu. Method of making high energy beam sensitive glasses, US Patents No , January 7, 99 (filed on November 4, 989). 4. S. Morton. The finbest gray scale yet, IEEE Spectrum., p.68, October C. Wu. High Energy Beam Sensitive Glasses, US Patents No , No , No , No , and No W. Daschner, P. Long, R. Stein, C.Wu, and S.H. Lee, Cost-effective mass fabrication of multilevel diffractive optical elements by use of a single optical exposure with a gray-scale mask on high-energy beam-sensitive glass, Appl. Opt., 36, N, pp , Canyon Materials Inc. Product information No LDW-glass photomask blanks. 8. M.R. Wang and X.G. Huang, Subwavelength-resolvable focused non-gaussian beam shaped with a binary diffractive optical element, Appl.Opt., 38, N, pp.7-76, V.P. Korolkov, A.I. Malyshev, V.G. Nikitin, V.V. Cherkashin, A.G. Poleshchuk, A.A. Kharissov, Application of gray-scale LDW-glass masks for fabrication of high-efficiency DOEs, Proceedings SPIE, 3633, pp.9-38, T. Fujita, N. Nishihara, and J. Koyama, Blazed gratings and Fresnel lenses fabricated by electron-beam lithography, Optics Letters, 7, N, pp , 98.. V.V. Cherkashin, E.G. Churin, V.P. Koronkevich, A.G. Poleshchuk, V.P. Korolkov, A.A. Kharissov, A.V. Kirianov, V.P. Kirianov, V.M. Vedernikov, A.G. Verhoglad, and S.A.. Kokarev, Circular laser writing system - CLWS-3C, EOS Topical Meeting Digest Series// Diffractive Optics,, pp. -3, T. Hessler, M. Rossi, R.E. Kunz, and M.T. Gale, Analysis and optimization of fabrication of continuous-relief diffractive optical elements, Appl. Opt., 37, pp , 998.