Off-axis Telescope Research Articles

Differential method for freeform optics applied to two-mirror off-axis telescope design.

In this Letter, we present a method to design the freeform surfaces of an off-axis unobscured two-mirror telescope by integration of a system of differential equations. The system is derived from the differentiation of Fermat's path principle and is integrated as an ordinary differential equation problem. The method is used to design the freeform surfaces of a telescope whose performance is verified in off-the-shelf optical design software (Zemax).

Wide-field off-axis telescope for the Mesospheric Airglow/Aerosol Tomography Spectroscopy satellite.

We present the development of a compact f/7.3 (D=35 mm) three-mirror reflective telescope for the atmospheric-research microsatellite Mesospheric Airglow/Aerosol Tomography Spectroscopy (MATS). The telescope design was driven by the end users' need for a reflective wide-field (5.67°×0.91°) optic with high stray light rejection and six detection channels with separate image sensors, operating at wavelengths 270-772nm. For the first time, a design method for wide-field off-axis telescopes-in which linear astigmatism is eliminated-was applied and tested in practice. Single-point diamond turning was used to produce two sets of 37-110mm large free-form aluminum mirrors with surface figure errors and roughness values of 34-62nm (RMS)/193-497nm (PV) and 2.8-3.5nm (RMS), respectively. A method that combines precise machining and geometry measurements (using a coordinate measuring machine) was employed to fabricate an aluminum structure to accurately position the mirrors without the need for manual alignment. The telescope was tested with a network of plate beamsplitters and filters, which define the spectral selection for the six detection channels. Imaging performance measurements were carried out using a reflective off-axis collimator, which projects imaging targets at infinite focus. A modulation transfer function (MTF) value of 0.45 at 20lp/mm was measured at ∼760 nm (diffraction limit: 0.85) using a slanted edge target. By modeling the measured mirror surfaces in optical design software, a reoptimization of the mirror positions could be performed and an improved MTF of ∼0.75 at 20lp/mm was predicted. The results demonstrate design- and building methods that can be utilized to make off-axis telescopes for a vast range of applications.

Aberration fields of off-axis astronomical telescopes induced by rotational misalignments.

Due to the absence of rotational symmetry, off-axis astronomical telescopes with off-set pupil become subject to rotational misalignments. Rotational misalignments of large off-axis mirrors with reference to their geometric center can greatly degrade the imaging quality. This paper presents an in-depth discussion on the net aberration fields of off-axis astronomical telescopes induced by rotational misalignments. Aberration function of off-axis telescopes with rotational misalignments is derived based on the framework of nodal aberration theory. Expressions of several important aberrations are obtained under some approximations. Then the specific field characteristics of these aberrations are presented and explicated. Meanwhile, we demonstrate that rotational misalignments can be converted to a kind of surface decenters; on the other hand, the effects of rotational misalignments have their special features which are different from the effects of general surface decenters. Besides, some other insightful discussions are further presented. This work is also applicable to the rotational misalignments of the off-axis segments of primary mirror in segmented mirror astronomical telescopes.

Vortex coronagraphs for the Habitable Exoplanet Imaging Mission concept: theoretical performance and telescope requirements

The Habitable Exoplanet Imaging Mission (HabEx) concept requires an optical coronagraph that provides deep starlight suppression over a broad spectral bandwidth, high throughput for point sources at small angular separation, and insensitivity to temporally-varying, low-order aberrations. Vortex coronagraphs are a promising solution that perform optimally on off-axis, monolithic telescopes and may also be designed for segmented telescopes with minor losses in performance. We describe the key advantages of vortex coronagraphs on off-axis telescopes: 1) Unwanted diffraction due to aberrations is passively rejected in several low-order Zernike modes relaxing the wavefront stability requirements for imaging Earth-like planets from <10 to >100 pm rms. 2) Stars with angular diameters >0.1 $\lambda/D$ may be sufficiently suppressed. 3) The absolute planet throughput is >10%, even for unfavorable telescope architectures. 4) Broadband solutions ($\Delta\lambda/\lambda>0.1$) are readily available for both monolithic and segmented apertures. The latter make use of grayscale apodizers in an upstream pupil plane to provide suppression of diffracted light from amplitude discontinuities in the telescope pupil without inducing additional stroke on the deformable mirrors. We set wavefront stability requirements on the telescope, based on a stellar irradiance threshold set at an angular separation of 3$\pm$0.5 $\lambda/D$ from the star, and discuss how some requirements may be relaxed by trading robustness to aberrations for planet throughput.

Compensation factors for 3rd order coma in three mirror anastigmatic (TMA) telescopes.

Misalignment induced third-order coma with respect to misaligned parameters in TMA optical systems is derived by using Nodal Aberration Theory, which yields the compensation factors that can be used to accomplish coma compensation in both coaxial and off-axis misaligned TMA telescopes. By using the compensation factors, coma free point for the tertiary mirror in TMA telescopes is derived and proved to be the negative form of the one for the secondary mirror in the Cassegrain telescope. The compensation factors can also be used to design the off-axis TMAs due to their capability of eliminating the coma over the field of view.

Optical compensation for the perturbed three mirror anastigmatic telescope based on nodal aberration theory.

In this paper, the Zernike coefficient is analytically expressed as the product of the dependence of aberration field decenter vectors (related with perturbations) and the dependence of fields of view (FOVs), on the frame work of nodal aberration theory (NAT). By expanding and analyzing this expression, an alignment strategy by optical compensation for the perturbed on-axis or off-axis telescope is presented. Specifically, two cases, corresponding to the misalignment of tertiary mirror (TM) and the deformation of primary mirror (PM), respectively, are discussed for the same three mirror anastigmatic (TMA) telescope. Here the misaligned TM and the deformed PM are compensated only by aligning secondary mirror (SM). By analyzing the aberration field after compensation with the nominal, it is found that either PM or TM can be compensated by SM. It is also found TM is more easily compensated than PM. In the end, the NAT method developed here used for optical compensation is compared to merit function regression (MFR) method and sensitivity table method (STM). By comparing NAT method with MFR method, it is shown that the calculated correction values of SM based on NAT method is very close to the referred values obtained from MFR method. It proves the correctness of NAT method developed here. By comparing NAT method with STM, it demonstrates that the computation accuracy of NAT method is much higher in poor conditions and NAT method is less sensitive to measurement errors. It is further illustrated that the theory of optical compensation by SM developed here is correct and applicable.

Active optical alignment of off-axis telescopes based on nodal aberration theory.

Our paper mainly separates the specific aberration contributions of third-order astigmatism and third-order coma from the total aberration fields, on the framework of the modified nodal aberration theory (NAT), for the perturbed off-axis telescope. Based on the derived aberration functions, two alignment models for the same off-axis two-mirror telescope are established and compared. Among them, one is based on third-order NAT, the other is based on fifth-order NAT. By comparison, it is found that the calculated perturbations based on fifth-order NAT are more accurate. It illustrates that third-order astigmatism and third-order coma contributed from fifth-order aberrations can't be neglected in the alignment process. Then the fifth-order NAT is used for the alignment of off-axis three-mirror telescopes. After simulation, it is found that the perturbed off-axis three-mirror telescope can be perfectly aligned as well. To further demonstrate the application of the alignment method based on fifth-order NAT (simplified as NAT method), Monte-Carlo simulations for both off-axis two-mirror telescope and off-axis three-mirror telescope are conducted in the end. Meantime, a comparison between NAT method and sensitivity table method is also conducted. It is proven that the computation accuracy of NAT method is much higher, especially in poor conditions.

Aberration fields of off-axis two-mirror astronomical telescopes induced by lateral misalignments.

This paper presents a systematic and in-depth discussion for the aberration fields of off-axis two-mirror astronomical telescopes with an offset pupil that is induced by lateral misalignment. Based on the framework of nodal aberration theory and a system level pupil coordinate transformation, the aberration function for misaligned off-axis telescopes is derived. Some general descriptions for the misalignment-induced aberrations are presented. The specific astigmatic and coma aberration field characteristics in off-axis two-mirror telescopes are then discussed. The precision of the presented aberration expressions is demonstrated. The discrepancies between the ray tracing data and aberration expressions are explicated. Then the inherent relationships between the astigmatism and coma aberration fields are revealed and explicated. Based on this knowledge, some quantitative discussions are further presented for determining the misalignments used to compensate for the effects of primary mirror astigmatic figure errors as well as separating these two effects when coupled. Other effects of lateral misalignments are also presented, especially the field-constant focal shift, which is only sensitive to the lateral misalignments in the symmetry plane of the nominal off-axis system. A quantitative discussion is also presented which explains the reason why trefoil aberration in off-axis telescopes is more sensitive to lateral misalignments. Most of the results presented in this paper can be extended to the other off-axis astronomical telescopes with more freedoms.

Development of an off-axis TMA telescope for coastal water remote sensing

A proto-model of an off-axis reflective fore-optics in a new hyperspectral sensor onboard a small unmanned aerial vehicle (UAV) is developed for low-altitude coastal remote sensing. In spite of the substantial advantages of off-axis optics over refractive or on-axis reflective optics, it is difficult to fabricate and align the mirrors in off-axis systems because of their asymmetric configurations. The fore-optics is designed by Korea Institute of Ocean Science & Technology (KIOST) as a three-mirror system including aspheric primary and secondary mirrors, with an entrance pupil diameter of 70 mm and F-ratio of 5.0. The off-axis mirror is fabricated by a single point diamond turning machine (SPDTM) with a form accuracy of 89.3 nm (RMS) and surface roughness of 7.2 nm (Ra). Coarse alignment of this three-mirror off-axis optical system is accomplished by using a designated base plate and a coordinate measuring machine. The optical performance is tested using the point spread function of the returned collimated beam of a Fizeau interferometer.

BFORE: The B-mode Foreground Experiment

The B-mode Foreground Experiment (BFORE) is a proposed NASA balloon project designed to make optimal use of the sub-orbital platform by concentrating on three dust foreground bands (270, 350, and 600 GHz) that complement ground-based cosmic microwave background (CMB) programs. BFORE will survey ~1/4 of the sky with 1.7 - 3.7 arcminute resolution, enabling precise characterization of the Galactic dust that now limits constraints on inflation from CMB B-mode polarization measurements. In addition, BFORE's combination of frequency coverage, large survey area, and angular resolution enables science far beyond the critical goal of measuring foregrounds. BFORE will constrain the velocities of thousands of galaxy clusters, provide a new window on the cosmic infrared background, and probe magnetic fields in the interstellar medium. We review the BFORE science case, timeline, and instrument design, which is based on a compact off-axis telescope coupled to >10,000 superconducting detectors.

Fabrication of electroless nickel plated aluminum freeform mirror for an infrared off-axis telescope.

Freeform mirrors can be readily fabricated by a single point diamond turning (SPDT) machine. However, this machining process often leaves mid-frequency errors (MFEs) that generate undesirable diffraction effects and stray light. In this work, we propose a novel thin electroless nickel plating procedure to remove MFE on freeform surfaces. The proposed procedure has a distinct advantage over a typical thick plating method in that the machining process can be endlessly repeated until the designed mirror surface is obtained. This is of great importance because the sophisticated surface of a freeform mirror cannot be optimized by a typical SPDT machining process, which can be repeated only several times before the limited thickness of the nickel plating is consumed. We will also describe the baking process of a plated mirror to improve the hardness of the mirror surface, which is crucial for minimizing the degradation of that mirror surface that occurs during the polishing process. During the whole proposed process, the changes in surface figures and textures are monitored and cross checked by two different types of measurements, as well as by an interference pattern test. The experimental results indicate that the proposed thin electroless nickel plating procedure is very simple but powerful for removing MFEs on freeform mirror surfaces.

연안 원격탐사를 위한 비축 삼반사경 설계와 성능 분석

We report the design and performance analysis of an off-axis three-mirror telescope as the fore optics for a new hyperspectral sensor aboard a small unmanned aerial vehicle (UAV), for low-altitude coastal remote sensing. The sensor needs to have at least 4 cm of spatial resolution at an operating altitude of 500 m, field of view (FOV), and a signal to noise ratio (SNR) of 100 at 660 nm. For these performance requirements, the sensor`s optical design has an entrance pupil diameter of 70 mm and an F-ratio of 5.0. The fore optics is a three-mirror system, including aspheric primary and secondary mirrors. The optical performance is expected to reach in RMS wavefront error and 0.75 in MTF value at 660 nm. Considering the manufacturing and assembling phase, we determined the alignment compensation due to the tertiary mirror from the sensitivity, and derived the tilt-tolerance range to be 0.17 mrad. The off-axis three-mirror telescope, which has better performance than the fore optics of other hyperspectral sensors and is fitted for a small UAV, will contribute to ocean remote-sensing research.

改进的灵敏度矩阵法在离轴望远镜装调中的应用

改进的灵敏度矩阵法在离轴望远镜装调中的应用

Optics ellipticity performance of an unobscured off-axis space telescope.

With the development of astronomy, more and more attention is paid to the survey of dark matter. Dark matter cannot be seen directly but can be detected by weak gravitational lensing measurement. Ellipticity is an important parameter used to define the shape of a galaxy. Galaxy ellipticity changes with weak gravitational lensing and nonideal optics. With our design of an unobscured off-axis telescope, we implement the simulation and calculation of optics ellipticity. With an accurate model of optics PSF, the characteristic of ellipticity is modeled and analyzed. It is shown that with good optical design, the full field ellipticity can be quite small. The spatial ellipticity change can be modeled by cubic interpolation with very high accuracy. We also modeled the ellipticity variance with time and analyzed the tolerance. It is shown that the unobscured off-axis telescope has good ellipticity performance and fulfills the requirement of dark matter survey.

Highly sensitive telescope designs for higher contrast observations

Abstract Off-axis telescope concepts that use unobstructed pupils have better emissivity, throughput, diffraction-limited energy concentrations, and higher dynamic range than traditional concentric instruments. The coronagraphic performance of off-axis telescopes will enable instruments, which are starved for higher dynamic range, for example, those devoted to faint companion detection, circumstellar and solar atmosphere studies.

Tandem gratings spectrometer for spectroscopy broadband anastigmatic imaging

A tandem gratings spectrometer with high imaging quality is designed. By applying the geometric analysis, the spectral broadband anastigmatic imaging conditions have been obtained. It offers an advanced design with low aberrations for the whole spectral range of the small-scale spectrometer both in the off-axis and coaxial telescope applications. A UV design exhibiting excellent optical performance is presented. The specifications of design have also been investigated.

宽视场航空高光谱成像仪光学系统设计

Airborne ocean colour remote sensing urgently require wide angle and large relative-aperture hyperspectral imager. Based on the research objective of wide angle and large relative-aperture, an airborne hyperspectral imager optical system was designed using an off-axis two-mirror anastigmat telescope and a modified Offner spectrometer. The field of view of hyperspectral imager was 40, relative-aperture was 1/2.2, and working waveband was from 0.4 m to 1m. Relative aperture and image quality were improved by inserting a concentric meniscus in a classical Offner spectrometer. Ray tracing, optimization and analysis were performed by ZEMAX software. The analyzed results demonstrate that the MTF for different wavelengths is more than 0.67 at Nyquist spatial frequency 28 lp/mm, both smile and keystone are less than 6.5% of the size of pixel. It is easy for spectral and radiation calibration. The design results satisfy the requirements of specifications, the volume is small, mass is low, and is suitable for airborne remote sensing.

Telescope design for 2 μm spacebased coherent wind lidar system

The telescope is a key optical component which largely affects the signal intensity in coherent Doppler Lidar. In the paper the normalized signal to noise ratio(SNR) as a function of range z and diameter D of the telescope is investigated for pulsed coherent wind lidar, then the telescope aperture requirement for 300km orbit is calculated and presented. After that the initial structure parameters for space-based (40×) off-axis telescope are obtained with the PW method, furthermore, the initial structure has been optimized by the Zemax software. The telescope's RMS wavefront error is optimized to be less than 1/10λ (2μm), and the tolerance requirement is discussed. The designed structure of the telescope is simple and compact, can be easily applied to other similar fields due to its high portability.

Preface

The Project for On-Board Autonomy 2 (PROBA2) mission has been in orbit 3.5 years and has evolved from a successful technology demonstration platform to a solar-science observatory and will soon become a space-weather monitoring mission. Few satellites have been so versatile in use; this is all the more remarkable knowing that PROBA2 is only a cubicmeter in size, low-budget micro-satellite. Nobody could have guaranteed its broad popularity during the Summer of 2002, when researchers at the Royal Observatory of Belgium replied enthusiastically to ESA's call for instruments onboard the second satellite in the PROBA program. In that year, solar maximum was in full swing and ESA was preparing for a European wide Space Weather Applications Pilot Project. At the Centre Spatial de Liege and the Royal Observatory of Belgium, people were working on the design of a suite of large EUV imagers called Magritte with an innovative off-axis telescope layout. Also innovative sensors and new non-silicon detectors were being studied in technological projects such as the Blind to the Optical Light Detector (BOLD) program.

Apodized phase mask coronagraphs for arbitrary apertures

Phase masks coronagraphs can be seen as linear systems that spatially redistribute, in the pupil plane, the energy collected by the telescope. Most of the on-axis light must ideally be rejected outside the aperture to be blocked with a Lyot stop, while almost all off-axis light must go through it. The unobstructed circular apertures of off-axis telescopes make this possible but all major telescopes are however on-axis and the performance of these coronagraphs is dramatically reduced by the central obstruction. Their performance can be restored by using an additional optimally designed apodizer that changes the amplitude in the first pupil plane so that the on-axis light is rejected outside the obstructed aperture of the telescope. The numerical optimization model is built by maximizing the apodizer's transmission while setting constraints on the extremum values of the electric field that the Lyot stop does not block. The coronagraphic image is compared to what a non-apodized phase mask coronagraph provides and an analysis is made of the trade-offs that exist between the apodizer transmission and the Lyot stop properties. The existence of a solution and the mask transmission depend on the aperture and the Lyot stop geometries, and on the constraints that are set on the on-axis attenuation. The system throughput is a concave function of the Lyot stop transmission. In the case of a VLT-like aperture, apodizers with a transmission of 0.16 to 0.92 associated with a four-quadrant phase mask provide contrast as low as a few 1e-10 at 1 lambda/D from the star. The system's maximum throughput is 0.64, for an apodizer with an 0.88 transmission and a Lyot stop with a 0.69 transmission. Optimizing apodizers for a vortex phase mask requires computation times much longer than in the previous case, and no result is presented for this mask.