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Abstract
The diffraction efficiency, defined as the ratio of diffracted power to incident power, is one of the key working indicators for a computer-generated hologram (CGH). The CGH with high diffraction efficiency could suppress stray light and eliminate ghost images, thus improving interferometric performance in aspherical testing of low-reflectivity or large off-axis distance surfaces. However, the high-efficiency CGH is hard to precisely fabricate by traditional reactive ion etching and focusing ion beam, because it requires high etching depth with a high uniformity and sub-nanometric roughness in the glass, especially in the fabrication of a large CGH with an aperture of up to 300 mm. In this study, fabrication of the above-mentioned CGH was demonstrated via what we believe to be a new method called scanning homogenization etching (SHE), in which the ion source with a Gaussian energy distribution accurately scans the glass surface to realize homogenization etching. Different from controlling dwell time at each etching point, this paper proposes to control the scanning rate to achieve not only uniform but also quantitative depth removal in a single scan. Moreover, the depth errors in deep etching across the whole glass surface can be remarkably reduced due to homogenization effects introduced by multiple scanning etching. Finally, the target etching depth of 692.3 nm with an etching uniformity of 2.2% in the etching of a 300 mm CGH was achieved. The roughness of the etched and unetched area both have Ra values of 0.3 nm. The diffraction efficiency of working order is 39.998%, achieving 98.6% of the theoretical diffraction efficiency. In addition, the SHE is not limited by the aperture of the ion source, so it can achieve even larger diffractive optical elements with high diffraction efficiency and high accuracy.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
The computer-generated hologram (CGH) is a diffractive optical element designed to produce a diffracted wavefront of a particular shape, often to match the shape of a particular optic [1]. CGHs enable high-accuracy snapshot measurements of complex optical surfaces, such as cylinders, rotationally symmetric aspheres, conic sections and freeforms [2–8]. However, in the CGH testing of large aperture mirrors, there were used to exist local data missing induced by some problems such as stray light and ghost images. Generally, these problems could be solved by separating the diffraction orders via increasing tilt carrier frequency or defocus carrier frequency [9], but these methods will increase line density and decrease the precision of CGH, even exceed the line-width limit of the lithography [10].
This paper proposes to solve these problems by increasing the diffraction efficiency of the working order to suppress ghost images and stray light from non-working orders. However, it is very difficult to fabricate the high diffraction efficiency and high precision CGH which simultaneously has strict requirements for etching depth, etching depth uniformity and etching surface roughness. For example, under theoretical maximum diffraction efficiency of 40.528%, the achievable depth uniformity was only 5% by a commercial etching method such as reactive ion etching (RIE) or inductively coupled plasma (ICP). These methods also result in poor surface roughness [11–13], which is equivalent to etching depth error, and thus decreasing the precision of CGH [14,15]. In addition to the RIE and ICP method, focusing ion beam (FIB) is also the method for diffractive optical elements etching, but it has problems of limited etching area and low etching efficiency [16,17].
Based on the above problems, a new method called scanning homogenization etching (SHE) was proposed to fabricate high-precision CGH with high diffraction efficiency. The SHE is a physical etching process based on the scanning Ar ion source with Gaussian energy distribution [18]. Through scanning rate and scanning strategy control, we achieved not only uniform but also quantitative depth removal across the whole glass surface. Finally, the target etching depth of 692.3 nm with an etching uniformity of 2.2% in the glass was achieved, realizing 98.6% of the theoretical maximum diffraction efficiency.
2. High diffraction efficiency CGH
A CGH with a diameter of 300 mm was designed for a 3.5 m SiC aspherical mirror. The optical path of CGH is shown in Fig. 1. The Lfc shows the difference between the focal plane of the interferometer and the front surface of the CGH substrate, while the Lcm shows the distance between the rear surface of CGH and the vertex of the 3.5 m mirror. The fringes calculated in each diffraction area of CGH were discretized and encoded in GDSII file format to obtain the GDS file of the CGH [19].
In the CGH testing of large-aperture aspheric and freeform mirrors, there were used to exist some problems such as stray light and ghost images. As shown in Fig. 2(a), due to the influence of the interference fringes from non-working orders, local data missing occurs at the edge of the error map, which is one of the manifestations of ghost images. As shown in Fig. 2(b), because the high energy non-working orders are not completely separated, local data missing occurs around the non-working orders, which is one of the manifestations of stray light. It was found that improving the diffraction efficiency of the working order can suppress ghost images and stray light from non-working orders.
In order to improve the diffraction efficiency, the mathematical model of CGH is analyzed, which is a binary, linear grating model based on typical diffractive optical elements [20,21], as shown in Fig. 3. The model is defined by grating period S and etching depth h. The duty cycle of the grating is defined as D = d/S, where d is the width of the unetched area. A0 and A1 correspond to the output wavefront amplitude of the etched area and unetched area of the grating, respectively. The phase depth ϕ represents the phase difference between these two areas. n is the refractive index of the grating substrate.
For a normal incident plane wavefront, the output wavefront function can be written as:
The far-field diffraction wavefront distribution of the outgoing wavefront of different orders can be written as:
The diffraction efficiency η is defined as the ratio of the intensity of the diffracted wavefront to the total intensity of the incident wavefront. As functions of duty cycle and phase depth, both the zero-order and nonzero-order diffraction efficiency expressions were utilized in fitting the measured intensities.
In order to achieve high diffraction efficiency, the design order of the main hologram is 1st, the phase depth is π, and the etching depth can be expressed as
3. Fabrication of CGH
3.1 Fabrication process
In this paper, a two-step method is proposed to fabricate the CGH. The specific fabrication process is shown in Fig. 4. The first step is pattern generation using laser direct writing followed by development on photoresist. Moreover, hardbaking is performed to remove the residual solution on the surface and improve the adhesion and anti-etching ability of the photoresist. The second step is pattern transfer using wet etching followed by scanning homogenization etching into fused silica. Importantly, the depth errors in deep etching across the whole glass surface can be remarkably reduced due to homogenization effects introduced by multiple scanning etching.
3.2 Scanning homogenization etching
As shown in Fig. 5(a), the ion beam source has a Gaussian-shape energy distribution [22]. Ar ions emitted by the ion beam source act with atoms on the workpiece surface to achieve a pure physics removal [23,24]. Different from RIE and ICP, the ion beam diameter was far smaller than that of CGH substrate. The whole glass surface can be etched by scanning the ion beam source along X and Y direction, and a quantitative depth removal can be achieved by scanning rate control. According to the traditional deconvolution method [25]:
where h(x, y) is the calculated etching depth distribution, R(x, y) is the removal function distribution, and T(x, y) is dwell time distribution of the ion beam during the etching process. Moreover, multiple scanning etching with different paths remarkably improve the depth uniformity across the whole glass surface.
Fig. 5. Scanning homogenization etching: (a) schematic of the SHE process; (b) position mode scanning; (c) speed mode scanning.
Generally, the dwell time in ion beam etching could be realized by the position mode. As shown in Fig. 5(b), the ion source moves rapidly between adjacent etching points to realize the accurate dwell time [26]. However, due to the speed and acceleration limitations of movement, it is difficult to stop etching between two adjacent etching points. Therefore, the additional depth method is often used in position mode scanning to solve this problem. However, the additional depth method directly reduces the etching efficiency. At the same time, due to the increase of etching time, the cumulative thermal effect becomes more serious and affects the etching precision.
As shown in Fig. 5(c), this paper proposes to convert the calculated dwell time into the scanning rate during the etching to realize accurate depth etching without additional depth and the cumulative thermal effect. The quantitative depth removal was achieved by controlling the scanning rate, and the uniform depth removal across the whole glass surface was achieved by multiple scanning etching with different paths. Furthermore, in order to improve the etching stability, the etching range is set to 150% of the CGH diameter, leaving space to achieve stable and uniform scanning.
To verify the stability and accuracy of speed mode scanning, the etching testing of fused silica plate with a diameter of 300 mm was carried out. The parameters of the ion source are shown in Table 1. Figure 6(a) and 6(b) show the change of surface profile of the plate before and after etching. By subtracting the two data sets, the error map of etching process shows in Fig. 6(c). The etching instability is smaller than RMS 0.004λ (λ=632.8 nm), which demonstrates the ability of scanning homogenization etching to create large-sized and high-precision CGH. Based on above parameters selection, the CGH with a diameter of 300 mm as shown in Fig. 7 was fabricated.
Table 1. Parameters of ion source for stability testing experiment
Fig. 6. Surface profile of the glass plate result: (a) before etching; (b) after etching; (c) etching instability.
4. Performance test
4.1 Etching precision
The etching precision of CGH includes etching depth accuracy, etching depth uniformity and etching surface roughness. The etching surface was observed by confocal microscope (Olympus, OLS 4100) under 100x magnification. Figure 8(a) show a typical groove topography of the 300 mm CGH. It can be seen that the grooves were clearly fabricated with uniform depth and smooth surface. In order to characterize etching depth and uniformity of the CGH, the whole surface was tested at a sampling interval of 20 mm. As shown in Fig. 8(b), the etching depth of the whole surface ranges from 686.2 nm to 701.1 nm, and the overall uniformity is less than 2.2%. The mean square deviation of etching depth in the full aperture is 2.86 nm. Moreover, the roughness of the unetched area and etched area were tested by white light interferometer (Zygo, New View 9000). As shown in Fig. 8(c) and 8(d), the etched surface roughness was not changed with the same Ra values of 0.3 nm. In summary, scanning homogenization etching shows excellent performance in etching uniformity and etching roughness, and thus has great advantages in the fabrication of high precision phase CGH.
where U is etching depth uniformity, ${X_i}$ is the etching depth of the whole surface and $\overline X$ is the average value of etching depth.Fig. 8. Test results of CGH with a diameter of 300 mm: (a) groove topography; (b) etching depth; (c) roughness of unetched area; (d) roughness of etched area.
4.2 Diffraction efficiency
Increase of diffraction efficiency on working order could solve the problems of ghost image and stray light from non-working orders. Figure 9 shows the testing optical path of diffraction efficiency. Throlab-pm201 optical power meter was used to measure the light intensity. A variable pinhole was placed in front of the focus of the 1st order to effectively reduce the influence of diffracted light from non-working orders on the light intensity measurement of working order.
The diffraction efficiency is defined as the ratio of the intensity between the 1st diffraction intensity of CGH and the transmitted light intensity of the CGH substrate.
where $\eta $ is maximum diffraction efficiency, ${E_1}$ is the 1st diffraction intensity of CGH at wavelength 632.8 nm and ${E_0}$ is the transmitted light intensity of the CGH substrate.Theoretically, the 1st order diffraction efficiency of phase type CGH is 40.528%. The diffraction efficiency at 20 different positions as shown in Fig. 10 were measured. The average diffraction efficiency is 39.998%, achieving 98.6% of the theoretical diffraction efficiency, which indicates that the diffraction efficiency of CGH has reached the maximum value.
Using the fabricated CGH, the 3.5 m SiC aspherical mirror with large off-axis distance was tested. Figure 11 shows the test result and interference fringes. It can be seen that the ghost images and stray light were completely eliminated. The fringes are very clear and their contrast is good enough for interference testing, indicating that the CGH has a high diffraction efficiency at working order. The surface shape precision of the 3.5 m mirror is RMS 0.016λ, indicating that the CGH was accurately fabricated.
5. Conclusions
In this paper, a new method called scanning homogenization etching is proposed to fabricate the CGH with highest diffraction efficiency. The following conclusions were drawn:
- 1. Due to homogenization effects introduced by multiple scanning etching, scanning homogenization etching can realize not only uniform but also quantitative removal of fused silica.
- 2. In the etching of a 300 mm CGH, an etching depth of 692.3 nm with an etching uniformity of 2.2% was achieved, which is remarkably better than that of 5% in the former reported methods.
- 3. Different from the etching by F-based gases, the pure physical etching by Ar ions in scanning homogenization etching makes the etched surface have the same roughness of Ra 0.3 nm as the unetched one.
- 4. Because of the accurate depth, high uniformity and sub-nanometer roughness of etched surfaces, the CGH diffraction efficiency of working order is 39.998%, achieving 98.6% of the theoretical diffraction efficiency.
- 5. Due to the high diffraction efficiency of the fabricated CGH, the stray light and ghost image were eliminated in testing the 3.5 m SiC aspherical mirror with large off-axis distance.
The scanning homogenization etching has almost no restriction on the material types and the aperture of the ion source, so it can achieve even larger micro-structured diffractive optical elements on a variety of materials with high diffraction efficiency and high accuracy. In future, the material removal rate of scanning homogenization etching will be optimized to reduce etching time.
Funding
National Key Research and Development Program of China (2020YFA0710100); National Natural Science Foundation of China (52375471, 62127901, 62305333, 62375260); Jilin Province Innovation and Entrepreneurship Talent Project (2023QN17).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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