Off-axis Paraboloid Research Articles

Compact off-axis reflective optical system design combining freeform mirror and freeform detector

Minimizing system size and weight without sacrificing the desired imaging performance is a crucial and challenging goal in the design of off-axis optical systems. In this paper, we propose a design concept that combines freeform mirror and freeform detector to achieve more compact off-axis optical systems. Initially, by applying nodal aberration theory, the optimal focal surface shape for off-axis systems is demonstrated to be an off-axis paraboloid or even a freeform surface, rather than the commonly assumed spherical shape. Subsequently, we show the ability of the design concept to reduce off-axis system volume through a design example of a fast and wide-field off-axis three-mirror system. Results indicate that, under the same design parameters and imaging quality, the design with a freeform detector is 80% smaller than that with a flat detector in terms of volume. Finally, the bending capability of the freeform detector presented in this paper is ensured through finite element analysis, and its surface accuracy is achievable based on the current precision level of curved detector fabrication. The proposed design concept holds promise for application in planetary science, where the imaging performance of the instrument is highly required and the size and weight are strictly limited.

Oblique-Incidence Interferometric Measurement of Optical Surface Based on a Liquid-Crystal-on-Silicon Spatial Light Modulator

An oblique-incidence interferometric measurement method is proposed to measure and adjust optical surfaces with a liquid-crystal-on-silicon spatial light modulator (LCoS-SLM). The optical system only consists of an interferometer and an LCoS-SLM with precision mounts. It could reduce the measuring cost and time consumption due to the programmable function of the LCoS-SLM and offer the ability to align the optical system. The oblique-incidence measurement theory and optical system adjustment method are established based on an off-axis paraboloid model. The ray-tracing program to calculate the compensation phase map in the measurement is proposed with math models. In the optical alignment step, the off-axis paraboloid model is used to apply the LCoS-SLM as a phase compensator to generate a focusing spot or light spot array to adjust the measured optical surface. And in the interferometric measurement step, the calculated compensation phase map from the ray-tracing calculation is loaded on the LCoS-SLM using the same optical setup as the optical alignment step without any mechanical adjustment. Two interference measurement experiments of typical optical surfaces were carried out to verify the accuracy of the measuring system.

Effect of Wheel Path in Raster Grinding on Surface Accuracy of an Off-Axis Parabolic Mirror

Off-axis parabolic mirrors have extensive applications in X-ray optics, with the precision of their curvature directly impacting grazing-incidence focusing performance. Notably, the off-axis parabolic surface has non-rotating and non-symmetrical characteristics. Ultra-precision raster grinding utilizing a diamond wheel is a common method. Crucially, establishing an optimal wheel path stands as the key to ensuring surface accuracy during off-axis paraboloid grinding. In this study, according to the double curvature property of an off-axis parabolic surface, two different wheel paths were compared: one tracing the meridian direction (parabolic generatrix) and the other following the arc vector direction (arc). The results showed that the wheel path in raster grinding stepping along the arc vector direction can obtain a smaller scallop height and higher surface accuracy. The surface accuracy of one step along the arc vector direction is 9.6 μm, and that of the other step along the meridian direction is 32.6 μm. A model of the scallop height was established based on the relative relationship between adjacent wheel paths, and the error is within 5%. According to the correlation between scallop height and shape error, we conducted an analysis of the spatial distribution of shape errors under varying wheel paths. The wheel path that steps along the arc vector is more suitable for raster grinding of the off-axis paraboloid. The above study can provide theoretical guidance for the wheel path planning of off-axis parabolic mirrors with high surface accuracy.

Continuous wave operation of terahertz metasurface quantum-cascade VECSEL with a long intra-cryostat cavity

We report continuous wave (cw) operation of a terahertz quantum-cascade vertical-external-cavity surface-emitting laser with an external cavity length of approximately 30 mm, benefited by an intra-cryostat focusing cavity. Compared to previous plano–plano cavities, an off-axis paraboloid mirror is introduced into the external cavity as a focusing element to reduce the diffraction loss and to enable cw lasing using small-area metasurfaces and long cavity lengths. The device shows lasing operation in the cw mode up to 111 K, and cw output power up to 11.5 mW at 77 K (0.5% wall-plug efficiency). A circular, directive beam pattern is collected, and free-running linewidths on the order of tens of kHz are measured over tens of seconds.

Green Bank Telescope: Overview and analysis of metrology systems and pointing performance

With a 100 m × 110 m off-axis paraboloid dish, the Green Bank Telescope (GBT) is the largest fully steerable radio telescope on Earth. A major challenge facing large ground-based radio telescopes is achieving sufficient pointing accuracy for observing at high frequencies, up to 116 GHz in the case of the GBT. Accurate pointing requires the ability to blindly acquire source locations and perform ad hoc corrections determined by observing nearby calibrator sources in order to obtain a starting position accurate to within a small margin of error of the target’s location. The required pointing accuracy is dependent upon the half-power beamwidth, and for the higher-frequency end of GBT observing, this means that pointing must be accurate to within a few arcseconds RMS. The GBT’s off-axis design is advantageous in that it eliminates blockage of the dish and reduces sidelobe interference, and there is no evidence that the resulting asymmetric structure adversely affects pointing accuracy. However, factors such as gravitational flexure, thermal deformation, azimuth track tilt and irregularity, and small misalignments and offset errors within the telescope’s structure cause pointing inaccuracies. A pointing model was developed for the GBT to correct for these effects. The model utilizes standard geometrical corrections along with metrology data from the GBT’s structural temperature sensors and data from measurements of the track levels. In this paper we provide a summary of the GBT’s pointing model and associated corrections, as well as a discussion of relevant metrology systems and an analysis of its current nighttime pointing accuracy.

Ultra-precision machining technology of off-axis paraboloid surface based on PMAC time-based control

Ultra-precision machining technology of off-axis paraboloid surface based on PMAC time-based control

In-situ deflectometric measurement of optical surfaces for precision manufacturing

The in-situ measurement of complex optical surfaces is a challenging task in precision engineering. The phase measuring deflectometry is a powerful measuring method for complex specular surfaces, and it has higher measuring efficiency, stability and dynamic range compared to interferometry. Consequently it is promising to widespread applications in various fields. Deflectometry is essentially a calibration problem, and the measuring accuracy is directly determined by the quality of geometrical calibration. An in-situ deflectometric measuring system is designed based on the single point diamond turning machine. A self-calibration method is developed to specify the relative positions of the camera and screen. Ray tracing is conducted at two positions of an auxiliary reflecting mirror, which is mounted on an air bearing spindle. The accuracy of the geometrical positions can be improved by an order of magnitude by minimizing the deviations of the traced points with respect to the true correspondences. According to the statistical properties of the deviations in reverse ray tracing, the form errors and the position errors can be separated, and the positioning error of the workpiece can be corrected accordingly. Henceforth, the nominal shape of the fabricated workpiece can be fully utilized, and the conventional one-way position-form mapping can be converted into a two-way mapping problem. As for the complex shapes, the whole surface can be covered by sub-aperture measurement. Precise localization of a local region under test is achieved by multi-position imaging, so that correct convergence of the iterative reconstruction process can be guaranteed. Several typical optical surfaces including an off-axis paraboloid mirror are measured, and the measuring accuracy of the proposed method is proved better than 150 nm RMS.

The Methods and Experiments of Shape Measurement for Off-Axis Conic Aspheric Surface.

The off-axis conic aspheric surface is widely used as a component in modern optical systems. It is critical for this kind of surface to obtain the real accuracy of the shape during optical processing. As is widely known, the null test is an effective method to measure the shape accuracy with high precision. Therefore, three shape measurement methods of null test including auto-collimation, single computer-generated hologram (CGH), and hybrid compensation are presented in detail in this research. Although the various methods have their own advantages and disadvantages, all methods need a special auxiliary component to accomplish the measurement. In the paper, an off-axis paraboloid (OAP) was chosen to be measured using the three methods along with auxiliary components of their own and it was shown that the experimental results involved in peak-to-valley (PV), root-mean-square (RMS), and shape distribution from three methods were consistent. As a result, the correctness and effectiveness of these three measurement methods were confirmed, which are very useful in engineering.

Compact adaptive interferometer for unknown freeform surfaces with large departure.

The newest experimental validation report of the coverage for the rotationally non-symmetric departure of a freeform surface in adaptive interferometry is about 20 µm. A compact adaptive interferometer is introduced to test unknown freeform surfaces with larger departure. The cascaded DMs (woofer and tweeter) can effectively double the measurable rotationally non-symmetric departure, to ∼80 µm using current DM technology. With a constrained decoupling control algorithm, the woofer and tweeter can averagely share the aberrations without coupling. DM surface monitoring is addressed by a time-division-monitoring (TDM) technique, which avoids separate monitoring devices and configurations and thus makes a compact configuration. Measurements of two different surfaces are presented: a nearly flat freeform with ∼40 um departure, and an off-axis paraboloid with ∼50 um of asymmetric departure.

Beam distortion effects upon focusing an ultrashort petawatt laser pulse to greater than 1022 W/cm2

When an ultrashort laser pulse is tightly focused to a size approaching its central wavelength, the properties of the focused spot diverge from the diffraction limited case. Here we report on this change in behavior of a tightly focused Petawatt class laser beam by an F/1 off-axis paraboloid (OAP). Considering the effects of residual aberration, the spatial profile of the near field and pointing error, we estimate the deviation in peak intensities of the focused spot from the ideal case. We verify that the estimated peak intensity values are within an acceptable error range of the measured values. With the added uncertainties in target alignment, we extend the estimation to infer on-target peak intensities of $\geq$ 10$^{22}$ W/cm$^{2}$ for a target at the focal plane of this F/1 OAP.

Metalized Poly-methacrylate Off-Axis Parabolic Mirrors for Terahertz Imaging Fabricated by Additive Manufacturing

Terahertz radiation sources are currently one of the most widely used non-ionizing illumination mechanisms for security applications and also find increasing utilization in quality control of commercial products. Presently, a majority of these applications rely on scanning rather than direct imaging and implicitly suffer from temporal latency due to post processing. The monetary and temporal cost associated with procuring commercially manufactured optics that are suitable for imaging leads to fundamental limitations in the ability to rapidly develop application-specific imaging modalities using terahertz sources. Herein, we show a novel method for the rapid prototyping of metallic coated poly-methacrylate parabolic reflectors fabricated by stereolithographic 3D printing. Images comparing the performance of a commercially available off-axis parabolic reflector to our metalized poly-methacrylate prototype, which was designed to be identical to the commercially available mirror, are subsequently presented. The images show that at 530 GHz it is possible to produce a metalized poly-methacrylate off-axis paraboloid whose spatial beam profile is nearly identical to that of a commercially available equivalent.

In situ noncontact measurement system and two-step compensation strategy for ultra-precision diamond machining.

Ultra-precision diamond machining is a promising technique for non-rotationally symmetrical surfaces with sub-micrometer form accuracy. The measurement and compensation processes in the fabrication process must be conducted carefully to achieve high form accuracy. However, significant challenges remain to improve the measurement accuracy and machining efficiency. Because of the remounting process, the off-machine measurements would reduce the efficiency. On the other hand, contact-type measurements can cause physical damage to some soft materials. To overcome these problems, a noncontact on-machine measurement (OMM) system is developed using two optical probes, and a two-step compensation strategy is proposed to generate a modified tool path. To verify the accuracy of the proposed measurement system, OMMs were performed on a spherical mirror using this system and were later compared with off-machine measurements. To evaluate the compensation strategy, an off-axis paraboloid mirror was diamond-machined and compensated using the proposed method. The results show that the OMM system and compensation strategy are effective for improving the form accuracy while simultaneously enhancing the machining efficiency.

AFOCAL SYSTEMS FORMED BY MIRROR OFF-AXIS PARABOLOID

Mirror systems make it possible to reduce device dimensions and its weight while preserving high input aperture and these systems are characterized by a number of other advantages. Their significant disadvantage is a central screening of an entrance pupil that leads to lower image quality. The paper contains description of the investigations on afocal systems formed by eccentrically cut-out mirror paraboloids (off-axis mirrors) where aperture diaphragm is displaced in the meridian plane for a defined value and a central field point is located on the optical axis. The canonic Mersenne systems are accepted as base schemas (modules) for these compositions. The paper considers two types of such systems: visible increases – Г > 0 and Г < 0. Algorithms for calculation of centered afocal systems with two and four reflections have been written in the paper and the systems are free from spherical aberration, coma, astigmatism when an input pupil is located in superimposed focal planes of all parabolic mirrors. An aberration in curvature image has been additionally corrected in three-mirror quart-parabolic scheme which is a combination of two classical telescopic Mersenne systems. The paper presents schemes and calculation results. Two-mirror schemes with non-screened input pupil have been studied in the paper and in this case all the system remains centered and an aperture diaphragm is decentered for the distance Cm which is commensurable with the diaphragm size. The paper contains description of the investigated afocal schemes with four reflections from off-axis mirror paraboloids, a prepared algorithm for calculation, the obtained formulas for making combination of canonic afocal systems formed by two mirrors. Computer simulation in software environment Opal and Zemax has been carried out in the paper. Basic description has been prepared while using two alternative methods for the class of decentered systems and aberration characteristics and schematic solutions for telescopic systems without screening with two and four reflections have been ob-tained in the paper. Two-mirror afocal systems with low-powered magnification are of some interest for practical application as accessories for registering object lenses.

Relativistic electron acceleration by mJ-class kHz lasers normally incident on liquid targets.

We report observation of kHz-pulsed-laser-accelerated electron energies up to 3 MeV in the -klaser (backward) direction from a 3 mJ laser interacting at normal incidence with a solid density, flowing-liquid target. The electrons/MeV/s.r. >1 MeV recorded here using a mJ-class laser exceeds or equals that of prior super-ponderomotive electron studies employing lasers at lower repetition-rates and oblique incidence. Focal intensity of the 40-fs-duration laser is 1.5 · 1018 W cm-2, corresponding to only ∼80 keV electron ponderomotive energy. Varying laser intensity confirms electron energies in the laser-reflection direction well above what might be expected from ponderomotive scaling in normal-incidence laser-target geometry. This direct, normal-incidence energy spectrum measurement is made possible by modifying the final focusing off-axis-paraboloid (OAP) mirror with a central hole that allows electrons to pass, and restoring laser intensity through adaptive optics. A Lanex-based, optics-free high-acquisition rate (>100 Hz) magnetic electron-spectrometer was developed for this study to enable shot-to-shot statistical analysis and real-time feedback, which was leveraged in finding optimal pre-plasma conditions. 3D Particle-in-cell simulations of the interaction show qualitative super-ponderomotive spectral agreement with experiment. The demonstration of a high-repetition-rate, high-flux source containing >MeV electrons from a few-mJ, 40 fs laser and a simple liquid target encourages development of future ≥kHz-repetition, fs-duration electron-beam applications.

Diode laser-based standoff absorption measurement of water film thickness in retro-reflection

A dual-wavelength diode laser-based absorption sensor for standoff point measurements of water film thickness on an opaque surface is presented. The sensor consists of a diode laser source, a foil as backscattering target, and off-axis paraboloids for collecting the fraction of the laser radiation transmitted through the liquid layer via retro-reflection. Laser wavelengths in the near infrared at 1412 and 1353 nm are used where the temperature dependence of the liquid water absorption cross section is known. The lasers are fiber coupled and the detection of the retro-reflected light was accomplished through a multimode fiber and a single photodiode using time-division multiplexing. The water film thickness at a given temperature was determined from measured transmittance ratios at the two laser wavelengths. The sensor concept was first validated with measurement using a temperature-controlled calibration cell providing liquid layers of variable and known thickness between 100 and 1000 µm. Subsequently, the sensor was demonstrated successfully during recording the time-varying thickness of evaporating water films at fixed temperatures. The film thickness was recorded as a function of time at three temperatures down to 50 µm.

The Donor At The VLA

A storm has left a dusting on the Magdalene said to be visible on the western side of the range. But she’s only a hill rusting in open air. Or a body without a heart. On this road to the Gila, on the wayward side of Datil, wind rattles the bat-gates at the adits of the zinc mines like a sneeze of the substance abuser it is. A young driver going west might get blinded by brute sun just shy of the radio telescopes at the Very Large Array. She flips, gone out of control, and succumbs in the O.R. in Socorro. Her heart expertly harvested. Iced. Flown to Albuquerque... Snow softened the surfaces but I refused to bury my childhood that far from trees. The scopes indeed were huge. Who could say how they worked? Off-axis paraboloids detecting dark energy... I suspect they would have made my parents lonely.

A Design Study of an Off-axis Paraboloid Shaping Method for Central Receiver System Heliostats

Abstract The aberration of the heliostat shapes in the central receiver system can cause energy losses and limit their concentration abilities. Ideally the heliostat shapes should be off-axis paraboloids that adapt as a function of time and locations in the field.However, such heliostats are costly to realize. This paper proposed a heliostat design using a new shaping method that can approximately implement the adaptive off-axis paraboloids at a low cost. In this design, a simple offset-force loading mechanism bends a flat compliant mirror with two-dimensional tailored stiffness to form the sagittal and tangential curvatures simultaneously. It can be easily implemented by conventional manufacturing process and adjusted to location-based optimized shapes during assembly on site. A modular central receiver heliostat field in high-concentration application was modelled numerically. The results show substantial advantages of the location-only optimized design over the flat mirrors and uniform-stiffness mirrors. Anexperimental heliostat prototype was built to validate the concept. The mirror shapes were tested by coordinate measuring machines and outdoor solar concentrating experiments. The experiment results show that high performance could be achieved by the proposed design approach.

一种离轴抛物面镜像差校正镜组的设计

一种离轴抛物面镜像差校正镜组的设计

A composite optical system for a LED based headlamp low beam module

In this paper, we propose a composite optical system for automotive headlamps. The system is composed of a paraboloid collimating reflector, an off-axis paraboloid reflector, a baffle and an imaging len. By using a LED as the light source, precise light distribution can be achieved. When making ray-tracing simulation for the composite optical system in TracePro, a clear cut-off line can be seen on the measuring screen, as well as a hotspot at the centre. The power consumption for the LED light sources in this system is less than 10 W, resulting in an energy efficiency of more than 58% and a maximum illumination of 26.76 lux at the centre hotspot.

Fabrication of off-axis aspheric surfaces using a slow tool servo

Off-axis aspheric surfaces have been widely applied in optical systems, but it is difficult to fabricate this kind of optical surface with high quality. Slow tool servo is one of the methods for turning off-axis aspheric surfaces on-axis, which have a large travel range without an additional device. This paper presents a theoretical and experimental investigation on the 3D surface generation in single point diamond tuning using slow tool servo. The form error of off-axis paraboloid caused by tool centering error is analyzed and verified by cutting experiment.