Our linear astigmatism-free confocal off-axis collimator comprises two off-axis mirrors and one flat mirror with an aperture size of 73 mm and a focal length of 1200 mm. The off-axis mirrors, along with all other opto-mechanical parts, will be fabricated from the same material, such as aluminum alloy 6061-T6. This concept inherently creates an athermalized structure, meaning the entire system expands or contracts by the same amount as the thermal coefficient of expansion, ensuring that the image remains consistently in focus. We approached this collimator’s design as if it were an astronomical telescope, reversing the optical path directions, and conducted tolerance analysis using Optic Studio (ZEMAX) to define the opto-mechanical design requirements. The collimator’s target or telescope imaging sensor size is 4 × 4 mm, with a required imaging resolution of 13.7 cycles/mm at a wavelength of 750 nm. To achieve this, we divided the full field (4 × 4 mm) into 3 × 3 subfields, ensuring that the average Modulation Transfer Function (MTF) value exceeds 10%. We performed Monte-Carlo Simulations 5000 times to determine tolerance ranges with a 90% confidence level. Furthermore, we conducted stray light analysis for our off-axis collimator design. In comparison to typical on-axis Cassegrain designs, where baffles block some parts of the target rays and reduce intensity, our designed confocal off-axis collimator accommodates baffles without obstructing any light from the target.
We are under integrating off-axis freeform mirrors for the KASI Deep Rolling Imaging Fast Telescope Generation 1 (KDRIFT G1) using a coordinate measuring machine and assembly jig. The telescope is a confocal off-axis freeform threemirror system designed for the detection of extremely low surface brightness structures in the sky. The optical specifications of the K-DRIFT G1 are as follows: the entrance pupil diameter is 300 mm, the focal ratio is 3.5, and the field of view is 4.43° × 4.43°. During the integration stage, we used a coordinate measuring machine to measure the positions of the mirrors, flexures, and bezels within a tolerance range. Following the system integration, we will measure wavefront errors at several edge fields using an interferometer at 633 nm. In this paper, we briefly present the current status of the K-DRIFT G1 and the future plans for the project.
A mode matching telescope for an EPR squeezer was designed with confocal off-axis configuration. Coupling loss is calculated as 0.02%, and the fabrication is expected to be feasible based on sensitivity analysis and Monte-Carlo simulation.
The optical design of a 400 mm-aperture, f/3, three-mirror freeform telescope for the MESSIER surveyor mission is presented. PhoSim PSF (Point Spread Function) simulations of the linear astigmatism-free optical design and mirror surfaces’ microroughness modeling indicate good manufacturability.
We are developing the KASI-Deep Rolling Imaging Fast Telescope Generation 1 (K-DRIFT G1) based on the on-site performance assessment of the K-DRIFT pathfinder. The telescope is a confocal off-axis freeform three-mirror system designed for the detection of extremely low surface brightness structures in the sky. The optical specifications of the K-DRIFT G1 are as follows: the entrance pupil diameter is 300 mm, the focal ratio is 3.5, the field of view is 4.43° × 4.43°, and the image area is 81.2 mm × 81.2 mm with 10 μm pixels. We performed sensitivity analysis and tolerance simulations to integrate and align the system. We present the analysis results and development plan of the K-DRIFT G1.
We have developed the KASI-Deep Rolling Imaging Fast Telescope (K-DRIFT), adopting a 300 mm aperture off-axis freeform three-mirror design to detect faint and diffuse low-surface-brightness structures. By conducting the on-sky test observations and performing a series of simulations to analyze the performance of the K-DRIFT, we confirmed three main error sources causing optical performance degradation. The imaging performance of the K-DRIFT has successfully improved by correcting low-to-mid spatial frequency wavefront errors based on performance analysis results. This paper presents the K-DRIFT’s optical performance analysis algorithm and the optical performance improvement.
The conventional on-axis reflective systems suffer from a diffraction effect on the Point Spread Function (PSF) due to the secondary mirror obscuration. Meanwhile, the unobscured off-axis reflective systems’ imaging performance may be impacted by linear astigmatism aberration. The Linear Astigmatism Free-Three Mirror System (LAF-TMS) is a confocal off-axis reflective system that eliminates linear astigmatism and enables a wide Field of View (FoV). We present an enhanced design of LAF-TMS, called ”wide-wide”, which has an aperture of D=40mm, an effective focal length of f=75mm, and a wide FoV of 8.25°(Horizontal) × 6.21°(V ertical) combined with a wide spectral bandwidth capability suitable for Unmanned Aerial Vehicle (UAV) applications. To evaluate the performance of this compact and fast optical system design, we use the Photon Simulator (PhoSim) to model physically accurate PSF under different conditions of the mirror surface, mechanical environment, and atmosphere. As a benchmark, we compare and analyze the PhoSim PSF results with other ray tracing software such as Zemax and CodeV. Additionally, PhoSim is capable of simulating infrared spectral imaging cases with a user-defined Spectral Energy Distribution (SED), intensity, and emissivity of each pixel. The comprehensive simulation results demonstrate the high performance of the LAF-TMS with a wide-wide FoV and multispectral capabilities.
The prototype of KASI-Deep Rolling Imaging Fast-optics Telescope (K-DRIFT) pathfinder is a 300 mm confocal off-axis freeform three-mirror system that has been developed for the detection of extended low surface brightness (LSB; below μV = 28 mag arcsec-2) structures. Until now, it is still very difficult to observe the LSB features due to systematic errors introduced by natural and instrumental effects. To overcome these, we apply the confocal off-axis telescope design theory that removed linear astigmatism, and each mirror made of Zerodur is set as a freeform surface to remove the residual aberration. Through the design, we can get high-quality images in a wide field of view and minimize sky background fluctuations. The size of the entrance pupil of the telescope is 300 mm and the focal length is 1200 mm. The field of view of the telescope is ~1° × 1° and the size of the focal plane is 22.5 mm × 22.5 mm. We have measured root mean square wavefront errors of the system after integration of the mirrors, flexures, and housing. At off-axis fields, the maximum root mean square wavefront error before the alignment is 260 nm, and decreased to 115 nm after alignment. Alignment-induced astigmatism and coma were almost eliminated through the process. In this paper, we briefly present the integration and alignment process of the K-DRIFT pathfinder and the current status of the project.
Optical design of the wide field of view telescope is limited by obscuration of the secondary mirror in onaxis system and by serious linear astigmatism in conventional common off-axis system. We have developed an innovative off-axis reflective system in which the optical design is based on the confocal off-axis to completely compensate the linear astigmatism. The main objective of this paper is to compare alignment sensitivity of the confocal system to those of on-axis and common off-axis systems. All three optical designs are based on the classical Cassegrain reflecting telescope and have identical entrance pupil diameter of 1000 mm and F/8 focal ratio. Tilt and decenter of each optical component, and despace which indicates inter-mirror distance are considered as tolerancing parameters that are explored within fabrication tolerance ranges. Encircled energy diameter is evaluated as a criterion of the analysis while tilts of the secondary mirror and the focal position are set to the compensator. The statistical tolerancing method based on Monte-Carlo simulation is also performed to analyze system tolerances. From sensitivity analysis and Monte-Carlo simulation, we concluded that the confocal off-axis system is more sensitive than on-axis and common off-axis systems but it is a feasible system in terms of fabrication and alignment errors.
Linear Astigmatism Free - Three Mirror System (LAF-TMS) is a confocal off-axis system that eliminates linear astigmatism, which is the most critical aberration especially in the large field angle, and therefore, enables the telescope to have a wide field of view. Based on our experience with the telescope, we optimized the LAF-TMS for wavelength ranges of mid-wavelength infrared (3-5 µm) and long-wavelength infrared (8-12 µm) sensors onboard Unmanned Aerial Vehicles (UAVs). It has an entrance pupil diameter of 70 mm, a focal ratio of 1.4, and a wide field of view (FoV) of 6.20° × 4.68°, matching 10.9 mm × 8.2 mm sensor with 17 µ m sized pixels (LAF-TMS D70F1.4). The freeform mirrors of LAF- TMS D70F1.4 are optimized to eliminate the high order aberration. As a result, LAF-TMS D70F1.4 can achieve high- quality optical performance over a wide FoV without any additional correcting lenses. We performed the sensitivity analysis and the Monte-Carlo simulations as the feasibility study. During the sensitivity analysis and the Monte-Carlo simulation, decenter, tilt, despace, and surface RMS errors of three mirrors were analyzed. From the sensitivity analysis, we investigated 80% Energy Encircled Diameter by single factor perturbations. The system tolerance limits were calculated using the Monte-Carlo method with a normal distribution of errors. According to the results, we confirmed that the LAF-TMS D70F1.4 was feasible considering general fabrication and alignment tolerances.
Effects of light intensity on disparity for depth extraction in monochrome CMOS image sensor with offset pixel apertures are investigated. The technology consumes less power, since it does not use external light sources. The offset pixel apertures are integrated in each pixel of the monochrome CMOS image sensor to acquire the disparity for depth extraction. Because the monochrome CMOS image sensor does not contain color filters, the height of the pixel is lower than that of the CMOS image sensor with color filters, resulting in a better disparity. The monochrome CMOS image sensor with offset pixel apertures was designed and fabricated using 0.11 μm CMOS image sensor process. Disparity of the sensor has been measured under various light intensities. The sensor might be useful for three-dimensional imaging in outdoor applications with a simple structure.
A CMOS image sensor with off-center circular apertures for two-dimensional (2D) and three-dimensional (3D) imaging was fabricated, and its performance was evaluated, including the results of 2D and 3D images. The pixel size, based on a four-transistor active pixel sensor with a pinned photodiode, is 2.8 μm × 2.8 μm. Disparate images as well as focused images for depth calculation can be obtained using the designed pixel pattern. The pixel pattern is composed of one white subpixel with a left-offset circular aperture, a blue pixel, a red pixel, and another white subpixel with a right-offset circular aperture. The proposed technique was verified by simulation and measurement results using a point light source. In addition, the depth image was implemented by calculating the depth information from the 2D images.
Effects of aperture size on the performance of CMOS image sensor with pixel aperture for depth extraction are investigated. In general, the aperture size is related to the depth resolution and the sensitivity of the CMOS image sensor. As the aperture size decreases, the depth resolution is improved and the sensitivity decreases. To optimize the aperture size, optical simulation using the finite-difference time-domain method was implemented. The optical simulation was performed with various aperture sizes from 0.3 μm to 1.1 μm and the optical power with the incidence angle as a function of the aperture size was evaluated. Based on the optical simulation results, the CMOS image sensor was designed and fabricated using 0.11 μm CMOS image sensor process. The effects of aperture size are investigated by comparison of the simulation and the measurement results.
The 3-dimensional (3D) imaging is an important area which can be applied to face detection, gesture recognition, and 3D reconstruction. Many techniques have been reported for 3D imaging using various methods such as time of fight (TOF), stereo vision, and structured light. These methods have limitations such as use of light source, multi-camera, or complex camera system. In this paper, we propose the offset pixel aperture (OPA) technique which is implemented on a single chip so that the depth can be obtained without increasing hardware cost and adding extra light sources. 3 types of pixels including red (R), blue (B), and white (W) pixels were used for OPA technique. The aperture is located on the W pixel, which does not have a color filter. Depth performance can be increased with a higher sensitivity because we use white (W) pixels for OPA with red (R) and blue (B) pixels for imaging. The RB pixels produce a defocused image with blur, while W pixels produce a focused image. The focused image is used as a reference image to extract the depth information for 3D imaging. This image can be compared with the defocused image from RB pixels. Therefore, depth information can be extracted by comparing defocused image with focused image using the depth from defocus (DFD) method. Previously, we proposed the pixel aperture (PA) technique based on the depth from defocus (DFD). The OPA technique is expected to enable a higher depth resolution and range compared to the PA technique. The pixels with a right OPA and a left OPA are used to generate stereo image with a single chip. The pixel structure was designed and simulated. Optical performances of various offset pixel aperture structures were evaluated using optical simulation with finite-difference time-domain (FDTD) method.
A 3dimensional (3D) imaging is an important area which can be applied to face detection, gesture recognition, and 3D reconstruction. In this paper, extraction of depth information for 3D imaging using pixel aperture technique is presented. An active pixel sensor (APS) with in-pixel aperture has been developed for this purpose. In the conventional camera systems using a complementary metal-oxide-semiconductor (CMOS) image sensor, an aperture is located behind the camera lens. However, in our proposed camera system, the aperture implemented by metal layer of CMOS process is located on the White (W) pixel which means a pixel without any color filter on top of the pixel. 4 types of pixels including Red (R), Green (G), Blue (B), and White (W) pixels were used for pixel aperture technique. The RGB pixels produce a defocused image with blur, while W pixels produce a focused image. The focused image is used as a reference image to extract the depth information for 3D imaging. This image can be compared with the defocused image from RGB pixels. Therefore, depth information can be extracted by comparing defocused image with focused image using the depth from defocus (DFD) method. Size of the pixel for 4-tr APS is 2.8 μm × 2.8 μm and the pixel structure was designed and simulated based on 0.11 μm CMOS image sensor (CIS) process. Optical performances of the pixel aperture technique were evaluated using optical simulation with finite-difference time-domain (FDTD) method and electrical performances were evaluated using TCAD.
TMA-based obstruction-free off-axis three-mirror systems became popular recently. Although they provide good performance over wide field of view by employing freeform mirrors, the overall dimension and the size of the system are relatively large considering their aperture size and focal length. More compact design is possible in off-axis two-mirror systems combined with field-correcting lens. A linear-astigmatism-free two-mirror system with correcting lens provides a wide field of view in relatively small size. In this paper, design examples of compact wide field two-mirror systems with correcting lens are presented.
A simple closed-form equation for the elimination of linear astigmatism in off-axis three-mirror telescope and imaging
system is presented. Several practical design examples of telescope and auxiliary optics based on the equation are also
presented and compared to the similar designs reported previously.
The basic concept and fundamental result of a recently developed geometric aberration theory for classical off-axis
reflecting telescopes and imaging systems are presented. It is shown that a classical off-axis reflecting telescope can be
designed to have practically axially-symmetric optical property by eliminating the dominant aberration (linear
astigmatism) caused by the asymmetric geometry. A simple closed-form equation for elimination of linear astigmatism
is presented. Also, to show how the developed aberration theory can be applied to current and future telescopes, several
off-axis reflecting telescopes and imaging systems are designed and analyzed.
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