Off-axis Three-mirror Anastigmat Research Articles

Desensitization design of freeform off-axis TMA optical systems with configuration selection

The off-axis three-mirror anastigmatic (TMA) optical system has the advantages of eliminating all primary aberrations, having no aperture obscuration, no chromatic aberration, and good environmental adaptability, making it essential in high-performance optical instruments. Freeform surfaces, with their rich degrees of freedom (DOFs) in mathematical representation, positively affect the image quality and sensitivity of optical systems. When applied correctly to off-axis TMA optical systems, they can achieve fast F-numbers, large fields of view (FOVs), and long focal lengths. There are dozens of configurations for off-axis TMA optical systems, and freeform surfaces can be combined in numerous ways within these systems. This paper first analyzes the sensitivity of off-axis TMA optical systems with different configurations, selects the configuration with the lowest sensitivity, and combines it with a low sensitivity freeform surface combination to achieve high-performance freeform off-axis TMA optical systems with low sensitivity.

Improving neural-network-based prediction models for misalignment in off-axis three-mirror anastigmat telescopes

The performance of a telescope system heavily relies on the precise alignment of the mirrors. The off-axis three-mirror anastigmat (TMA) telescope presents unique challenges due to its complex optical design. Each optical element within the off-axis TMA telescope is inherently introduced with theoretical eccentricity and tilt. Furthermore, the incorporation of freeform surfaces and other optical elements with intricate surface features typically leads to low initial alignment accuracy of the optical path. With this low initial alignment accuracy and the noise of the measurements, the prediction of the misalignment of the telescope is getting harder. A fully connected neural network architecture is proposed as a misalignment calculation method for an off-axis TMA telescope system with a freeform surface. Random training data is created by using optical design software. The sensitivity of the mirrors to the wavefront error is quantified and incorporated into the loss function of the neural network to improve prediction accuracy. Adding the noisy measurement samples to the training data creates a noise-immune neural network model. Simulation results show that our model can successfully predict misalignment of the mirrors with noisy measurement values.

Design method for zoom systems based on magnification ratio modulation of afocal off-axis three-mirror anastigmat systems

Design method for zoom systems based on magnification ratio modulation of afocal off-axis three-mirror anastigmat systems

Design Method for Freeform Off-Axis Three-Mirror Anastigmat Optical Systems with a Large Field of View and Low Error Sensitivity

A freeform off-axis three-mirror anastigmat (TMA) optical system with a large field of view (FOV) can obtain target image information with a larger spatial range and more spatial details, which is a development trend within the realm of space optics. The optical aberration increases exponentially with the FOV, resulting in a significant increase in error sensitivity for large-FOV optical systems. To address this issue, a method for designing optical systems with a large FOV and low error sensitivity is proposed. The FOV is gradually expanded from a small initial value in equal-length increments until it reaches the full FOV. At each step, the error sensitivity is recalculated and controlled to a lesser extent than in the previous step. In this design process, the freeform surface is used to correct the aberration and obtain low error sensitivity. An optical system with a focal length of 1000 mm and an F-number of 10 is used as an example, and the FOV is enlarged from 5° × 1° to 20° × 4°. The design results show that the modulation transfer function (MTF) of the optical system can reach 0.45@50 lp/mm, and the average wavefront aberration is 0.029λ. After four rounds of FOV expansion and error sensitivity optimization, the error sensitivity is reduced by 37.27% compared to the initial system, which verifies the correctness and practicality of the method.

Optical Design of a Solar Simulator With Large Irradiation Surface and High Irradiation Uniformity

Aiming at the problem of low irradiation uniformity in existing solar simulators with large irradiation surface, a new optical design method of off-axis TMA (three-mirror anastigmat) solar simulators with large irradiation surface high uniformity was proposed. Three groups of short arc xenon lamps and non-coaxial ellipsoid mirror are used as composite light sources, the causes of stray light in optical integrator are clarified, and the optimization design method of integrator based on anti-crosstalk diaphragm is proposed. The light propagation matrix model of the optical system of the solar simulator is established to effectively suppress stray light in the integrator, and the influence of the aberration of the collimating system on the irradiation uniformity was analyzed. A optical system of object side telecentric off-axis TMA was designed to achieve high uniform illumination with large irradiation area. The results show that in the Φ500 mm irradiation surface, the irradiance of the system is better than 1S <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">0</sub> (1367 w/m <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> ), up to 1656 w/m <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> , irradiation uniformity is 98.29%, this research can provide accurate and reliable solar radiation for space environment experiment of satellite load and make up for the limitation of low irradiation uniformity of traditional solar simulators with large irradiation surface.

Misalignment algorithm of a wide-field survey telescope based on third-order quadratic nodal aberration theory

Off-axis three-mirror anastigmatic (TMA) telescopes with designed decenters and tilts, have many misalignment degrees of freedom and strong coupling between each misalignment degree of freedom. Therefore, it is difficult to establish misalignment equations only using A222 and A131 in nodal aberration theory (NAT). In addition, for off-axis TMA optical systems with designed decenters and tilts, the robustness of the existing fifth-order NAT misalignment calculation algorithm based on high-order Zernike coefficients and boresight errors decreases, so it is difficult to realize its engineering application. To solve the issue of insufficient practicality of the existing misalignment algorithm based on fifth-order NAT, a third-order NAT calculation algorithm based on quadratic aberration field decenter vectors is derived and established. Two concepts of inherent aberration field decenter vector and misalignment aberration field decenter vector are proposed. Taking an off-axis TMA optical system with 6-m focal length as the research object, simulations, and alignment verification experiments were carried out. Compared with the existing fifth-order NAT misalignment algorithm, the results show that when measurement noise is not considered, the two methods can both obtain convergent calculation results, and the average RMS wavefront errors (WFE) of the optical system are both corrected to be below 0.0574 waves. When different levels of measurement noise are introduced, the robustness of the fifth-order NAT misalignment algorithm decreases, and there are even cases where the optical system completely fails to be corrected. However, the algorithm based on quadratic aberration field decenter vectors shows better robustness. Under different levels of measurement noise, this algorithm could correct the average RMS WFE of the optical system to around 0.0574 waves.

Comparisons between an on-axis three-mirror anastigmat telescope and an off-axis one: polarization aberrations.

Due to the ability to achieve a wide-diffraction-limited field of view, three-mirror anastigmat (TMA) telescopes are widely used in many applications that demand high imaging quality and detection accuracy, in which polarization aberrations play increasingly important roles. In this paper, polarization properties of on-axis elements and those of off-axis elements are analyzed and compared via polarization aberration theory. Then, an on-axis TMA (OTMA) telescope and an off-axis TMA (FTMA) telescope are designed and optimized to be diffraction-limited systems in parallel. Their constructional parameters and first-order parameters are set to be identical. Via polarization ray tracing, polarization aberrations of the 2 telescopes are obtained and compared in terms of diattenuation map, retardance map, Jones pupil, Pauli pupil, and amplitude response matrix. Results demonstrate that polarization aberrations are closely related to the structural features of mirrors and telescopes. The diattenuation and retardance maps of power mirrors in the OTMA telescope are rotationally symmetric, while those in the FTMA telescope are not. A Maltese cross appears in off-diagonal elements of the Jones pupil of the OTMA telescope and disappears in the FTMA telescope. Amplitude response matrices of polarization crosstalk components in the OTMA telescope are with a four-peak structure, while those in the FTMA telescope are with a two-peak structure. After quantitative comparisons, it is found that diattenuation in the OTMA telescope is smaller than that in the FTMA telescope as well as in the cases of retardance and polarization crosstalk. There are also similarities between the 2 TMA telescopes. Polarization aberrations of secondary mirrors (SM) are greater than those of both primary mirrors (PM) and tertiary mirrors (TM). What is more, polarization aberrations of TM are so small that they can be ignored safely. The numerical sum of Pauli coefficients of PM, SM, and TM is nearly identical to the cumulative Pauli coefficients. Hence, the TMA telescopes can be treated as weak polarization elements. This work compares polarization aberration performance of on- and off-axis TMA telescopes and can provide important references for designing and optimizing telescopes in which polarization aberrations matter.

Aberration compensation strategy for the radius of curvature error of the primary mirror in off-axis three-mirror anastigmatic telescopes.

This paper discusses compensation strategies for the aberration fields caused by the error in the radius of curvature (ROC) of the primary mirror (PM) in pupil-offset off-axis three-mirror anastigmatic (TMA) astronomical telescopes. Based on the nodal aberration theory framework, the specific astigmatic and coma aberrations of the off-axis three-mirror system in the presence of the ROC error of the PM are derived. It is demonstrated that some field-dependent aberration components can be induced by ROC error in the off-axis TMA telescopes, apart from the dominating field-constant aberration terms. To reduce the influence of the ROC error on the aberration fields, we propose two aberration compensation strategies: adjusting the position of the PM and introducing axial misalignment of the secondary mirror (SM). Through theoretical analysis and simulations, we conclude that the compensation strategy of changing the axial position of the PM can make the aberration distribution close to the nominal state; the compensation strategy of axially adjusting the SM can make the aberration distribution meet the observation requirements, which is more suitable for space applications. We also discuss compensating the effect of the ROC error using lateral misalignments.

Stray light control and analysis for an off-axis three-mirror anastigmat telescope

Off-axis three-mirror anastigmat (TMA) telescopes provide excellent correction of aberrations over a large field-of-view in one direction. In a push broom configuration, this lightweight and compact optical configuration enables high-performing imaging. Moreover, passive multi-spectral acquisition can be achieved using a filter stack positioned at the detector vicinity. Stray light is a typical limiting factor for instrument performance and its control is specific to the type of optical configuration. We describe the stray light control and analysis methods in an off-axis TMA. The design intends to control first-order scattering from non-optical surfaces and to block straight shots. This is achieved through usage of elements such as apertures and baffles, both internal and external to the instrument. It will be demonstrated that the aperture stop is a critical element, whose stray light contribution can be controlled with V-groove vanes. Impact of mirrors roughness, a manufacturing physical limitation, is evaluated by modeling the bidirectional scattering distribution function and computing the stray light distribution at the detector for point-like source illumination. We show that the scattering on the different mirrors broaden differently the spot size, as the successive mirrors focus or expand the scattered rays differently. Finally, the ghost reflections inside the filter stack are evaluated and we show that there is no cross-talk between the different channels.

Design of biaxial flexural mount for a rectangular mirror with large aspect ratio of a space telescope

In this paper, the biaxial flexural mount is presented according to the requirements of the large aspect ratio mirror of an off-axis three-mirror anastigmatic (TMA) space-borne telescope, and the process of the optimal design of the flexural mount structure is discussed in detail. From the perspective of mechanics-based design of space-borne mirror assembly structure and integrated optical-mechanical analysis, the optimal axial mounting position, the optimal mounting angle and the optimal structural critical dimensions of the flexure hinge were determined to improve the surface shape accuracy. Finally, the mechanical vibration test further proved the rationality of the structure design and the accuracy of the simulation analysis. The flexural mount proposed in this paper is can be applied to other reflective optics with high surface figure requirements. The optimization method proposed in this paper can also be applied to the optimization of other forms of flexural mount.

Design of image-side telecentric off-axis three-mirror anastigmatic systems based on the coaxial parent mirrors

Image-side telecentric unobscured optical systems have significant application values in the field of space optics. However, off-axis astigmatism increases with an increase of field of view (FOV), relative aperture and image-side telecentricity, so it's very difficult to design image-side telecentric anastigmatic systems with an ultrawide FOV. To solve these issues, this paper proposes an effective method that is based on the coaxial parent mirrors. By calculating the off-axis aberration optical path of the primary mirror (PM), secondary mirror (SM) and tertiary mirror (TM), and introducing even aspheric surface and adding boundary constraints, a prospective system with a focal length of 400 mm, a relative aperture of 1/3, an FOV of 18° × 6°, and a telecentricity of greater than 0.5°is designed. The design results show that the modulation transfer function (MTF) of the system is greater than 0.7 at the Nyquist frequency of 34 lp/mm, which is close to the diffraction limitation. It has a high imaging quality, thereby proving the image-side telecentric off-axis three-mirror anastigmatic (TMA) system to be effective.

Design of a high-throughput telescope based on scanning an off-axis three-mirror anastigmat system.

A high-throughput optical system possesses a large field of view (FOV) and high resolution. However, it is a major challenge to design such a telescope with these two conflicting specifications. In this paper, we propose a method to design a high-throughput telescope based on the classical off-axis three-mirror anastigmat (TMA) configuration by introducing a scanning mechanism. We derive the optimum initial design for the TMA system with no primary aberrations through characteristic ray tracing. During the design process, a real exit pupil is necessitated to accommodate the scanning mirror. By gradually increasing the system's FOV during the optimization procedure, we finally obtained a high-throughput telescope design with an F-number of 6, a FOV of 60∘×1.5∘, and a long focal length of 876 mm. In addition, a tolerance analysis is also conducted to demonstrate the instrumentation feasibility. We believe that this kind of large rectangle FOV telescope with high resolution has broad future applications in the optical remote sensing field.

Improvement of a computer-aided alignment algorithm for the nonsymmetric off-axis reflective telescope

Due to complications of the off-axis three-mirror anastigmat (TMA) telescope, each optical element in the off-axis TMA telescope is introduced with theoretical eccentricity and tilt. Moreover, the introduction of freeform surfaces and other optical elements with complex surface features generally causes the initial alignment accuracy of the optical path to be low. A large initial alignment error amplifies the sensitivity of the misalignment calculation accuracy to the measurement error of the Zernike coefficient, resulting in difficulty obtaining convergence results for a computer-aided alignment algorithm. Considering the above issues, the alignment sensitivity of each component in the optical path is analyzed in this. The large conditional number of the sensitivity matrix results in poor algorithm robustness. Thus, an adaptive damping factor least-squares algorithm model is proposed and derived to improve the efficiency of the classical least-squares algorithm. A method for piecewise optimization of the damping factor is also deduced. Experiments based on a 0.6 m off-axis TMA telescope verify the effectiveness of the algorithm. Simulation and integration experiments show that the proposed method can reduce the accuracy requirements of the initial alignment and improve the adaptability of Zernike coefficient measurement noise. The alignment procedure is carried out for three iterations, and the average of the five field-of-view wave aberration values is enhanced from 2.1λ (RMS; λ=632.8nm) to 0.09λ (average). The improved algorithm can solve the large initial alignment error of a nonsymmetrical off-axis reflective optical system with a freeform surface as well as the problem of the low success rate of the misalignment value due to low Zernike coefficient measurement accuracy.

Analysis and test of transmit-receive isolation of off-axis three-mirror anastigmat optical antenna applied to laser communication

The bi-directional duplex working mode of a transmit-receive integrated optical antenna in laser communication systems has a rigorous requirement on transmission and receiver(T/R) isolation. By using an off-axis three-mirror anastigmat (TMA) optical antenna, backscattered can be significantly reduced, thus achieving high T/R isolation. This paper proposes to design the light exit angle of 5° or larger in the off-axis TMA optical antenna and use the equivalent surface roughness (ESR) to evaluate the surface scattering characteristics of reflector in optical antenna. Therefore, by increasing the ESR of reflector, the isolation of the optical antenna can be improved. In an isolation measurement experiment, the measured isolation of the F150mm off-axis TMA optical antenna was 73 dB, which is consistent with the simulation result. The achieved T/R isolation level meets the requirements for acquiring, tracking, and communication of satellite laser communication systems.

Experimental study on the extension of nodal aberration theory to pupil-offset off-axis three-mirror anastigmatic telescopes

The aberration fields of misaligned on-axis telescopes can be described by nodal aberration theory. However, traditional nodal aberration theory cannot directly apply to pupil-offset off-axis systems. In our previous work, the net aberration fields of pupil-offset off-axis two-mirror astronomical telescopes induced by lateral misalignments were investigated by extending nodal aberration theory to include pupil-offset off-axis telescopes with a system-level pupil coordinate transformation through simulation. An experimental study on the net aberration fields of pupil-offset off-axis three-mirror anastigmatic (TMA) telescopes induced by lateral misalignments is further presented. Specifically, the astigmatism and coma aberration fields as well as their inherent relations are analytically expressed, simulated, and quantitatively validated with a real pupil-offset off-axis TMA telescope. Meanwhile, the differences between the aberration fields of misaligned off-axis and on-axis TMA telescopes are revealed and explicated. Our work not only contributes to a deep understanding of the net aberration fields of pupil-offset off-axis TMA telescopes induced by lateral misalignments but also represent an important validation for the extension of nodal aberration theory to pupil-offset off-axis telescopes.

Thermal compensation design of truss structure for large-scale off-axis three-mirror space telescope

The image quality of the large-scale, long-focus, large field of view, off-axis three-mirror anastigmat space telescope will decrease dramatically due to the thermal effect. This paper studies the thermal deformation of the telescope, and based on its axial deformation, it proposes a passive thermal compensation design using truss rods made of carbon fiber-reinforced plastics, utilizing its thermal conducting design, which is determined by different spread quantity and spread angle of the lamination. Meanwhile, it satisfies the system stiffness requirement. First, the truss rods are divided into several independent triangles, according to the principle of equal axial distance after deformation, the function in terms of coefficient of thermal expansion (CTE) and length of truss rods is determined. Bonded by the optical tolerance requirement, the range of the CTE is obtained. Second, according to the CTE function, coupled with the stiffness requirement of the whole instrument, the CTE of each truss rod is determined. According to the CTE and stiffness requirement, the design of truss rods lamination is carried out. Finally, the group of truss rods with unequal CTE is obtained. The results have been validated by finite element analysis, vibration experiments, and image test, which indicate that the accuracy of the space telescope studied meets the requirements of optical tolerance; in addition, the rotation angle of the front panel around the X axis is competent, implying the stiffness requirement is solved. Moreover, the modulation transfer function at Nyquist frequency is better than 0.178 under the condition of 20 ° C ± 5 ° C.

Three-mirror anastigmat for cosmic microwave background observations.

An off-axis three-mirror anastigmat is proposed for future cosmic microwave background observations. The telescope has a 5m diameter primary, giving 1.5' angular resolution at λ=2 mm, which is sufficient for measurements of gravitational lensing and for galaxy cluster surveys. The design includes several key features, not previously combined in a large telescope, that are important for sensitive measurements, especially on large angular scales: (1)high throughput (8° diameter diffraction-limited field of view at λ=1 mm, and 12×8° at λ=3 mm, so a single telescope could support all the detectors for an optimistic, future experiment); (2)low scattering (all the mirrors are small enough to be monolithic, so there are no segment gaps); (3)full boresight rotation, over the full elevation range, for measuring polarization errors; and (4)a comoving shield or baffle around the entire telescope to control pickup.

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.

Design and optimization for main support structure of a large-area off-axis three-mirror space camera.

To ensure excellent dynamic and static performance of large-area, off-axis three-mirror anastigmat (TMA)-space cameras, and to realize a lighter weight for the entire system, a truss support structure design is applied in this study. In contrast to traditional methods, this paper adopts topology optimization based on the solid isotropic materials with penalization method on the truss structure design. Through reasonable object function and constraint choice, optimal topology results that have concerned the effect of gravity in the X, Y, and Z axis are achieved. Subsequently, the initial truss structure is designed based on the results and manufacturing technology. Moreover, to reduce the random vibration response of the secondary mirror and fold mirror without mechanical performance decline of the whole truss, a weighted optimization of truss size is proposed and the final truss structure is achieved. Finite element analysis and experiments have confirmed the reliability of the design and optimization method. The designed truss-structure camera maintains excellent static performance with the relative optical axis angle between the primary mirror and corresponding mirrors (secondary mirror and fold mirror) being less than 5.3 in. Dynamic performances, such as random and sinusoidal vibration responses, also met the requirements that the acceleration RMS value for mount points of the fold mirror should be less than 20 g and the primary frequency reached 97.2 Hz.

The alignment and imaging experiment of a telescope with wavefront coding technology

Wavefront coding (WFC) is kind of computational imaging technique that controls misfocus and misfocus-related aberrations of optical systems by appending a specially designed phase distribution to the pupil function. This technology has been applied in many fields to increase the performance or/and reduce the cost of imaging systems. The application of WFC technology on an off-axis three-mirror anastigmatic (TMA) system has been proposed in our previous work. In this letter, we describe the alignment, the imaging experiment and image restoration of an actual TMA system with WFC technology. 2014 中文 Optics Letters.