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The linear robot path is tangential and curvature discontinuity, which will lead to vibration and unnecessary hesitation during execution. Local corner transition method and local spline interpolation method are used in state-of-art industrial robot controller to reduce vibration, while local corner transition method cannot interpolate target points and local spline interpolation method cannot constrain chord errors. This research proposes a robot path local interpolation method that eliminates deficiencies of each method. The smoothing method satisfies all of the following requirements: G1 continuity, target point interpolation and chord tolerance confined, shape-preserving (free of self-intersection), and unified parameterization. The generated smooth path consists of linear path and circular arc path with G1 continuity. A geometric iterative method cooperating with local corner transition method is used to generate local interpolation path. Simulations and actual experiments verify the generated smooth path is G1 continuous, tolerance constrained, shape-preserving, and have high computational efficiency.

A single shot ptychographic iterative engine based on chromatic aberrations is proposed to retrieve the object with fast data acquisition and convergence. In the imaging system, the specimen is irradiated by a RGB illumination source, and the RGB light transmitted through the specimen is recorded by a color sensor. There are three different sizes of the spots on the object surface generated by the lens with chromatic aberrations and the aperture stop, which can produce partially overlapping between adjacent wavelength illumination areas that will lock the object’s phase information and ensure retrieve the object successfully. In the reconstruction algorithm, an initial object guess is established by spectrum synthesis method to accelerate convergence and suppress noise. The data acquisition time is dramatically reduced by our proposed single shot method.

Three-dimensional(3D) flame chemiluminescence tomography (FCT) is realized in multi-direction and multi-angle using traditional iterative algorithms. However, 3D-FCT is often challenged by insufficient sampling data because of the limited observation windows provided in practical for flame measurement. To obtain flame multiple projections in limited observation windows, we develop a camera array arrangement in FCT. In addition, a residual network with a new loss function combing physical model of flame is proposed to achieve higher reconstruction accuracy, faster reconstruction speed and efficient image feature in residual network for 3D FCT measurement. Furthermore, the determination of the weight coefficient in the loss function is performed by numerical simulation experiments. The flame reconstruction results show that the proposed residual network method including the new loss function has more reliable structural similarity and noise immunity compared with the ART algorithm and the CNN algorithm. This work provides a faster and more accurate method for combustion diagnosis under limited observation windows with insufficient projections.

The transverse resolution of optical coherence tomography is decreased by aberrations introduced from optical components and the tested samples. In this paper, an automated fast computational aberration correction method based on a stochastic parallel gradient descent (SPGD) algorithm is proposed for aberration-corrected imaging without adopting extra adaptive optics hardware components. A virtual phase filter constructed through combination of Zernike polynomials is adopted to eliminate the wavefront aberration, and their coefficients are stochastically estimated in parallel through the optimization of the image metrics. The feasibility of the proposed method is validated by a simulated resolution target image, in which the introduced aberration wavefront is estimated accurately and with fast convergence. The computation time for the aberration correction of a 512 × 512 pixel image from 7 terms to 12 terms requires little change, from 2.13 s to 2.35 s. The proposed method is then applied for samples with different scattering properties including a particle-based phantom, ex-vivo rabbit adipose tissue, and in-vivo human retina photoreceptors, respectively. Results indicate that diffraction-limited optical performance is recovered, and the maximum intensity increased nearly 3-fold for out-of-focus plane in particle-based tissue phantom. The SPGD algorithm shows great potential for aberration correction and improved run-time performance compared to our previous Resilient backpropagation (Rprop) algorithm when correcting for complex wavefront distortions. The fast computational aberration correction suggests that after further optimization our method can be integrated for future applications in real-time clinical imaging.

Diffracted wavefront measurements are qualitative and comprehensive verifications for the spherical grating that was manufactured to specifications. Direct interferometric testing of the diffracted wavefront is convenient and implemented by tilting the spherical grating at a Littrow angle to obtain autoreflection and then results in a nonnull interferometric testing configuration. The diffracted wavefront of the spherical grating contains not only wavefront errors induced by the manufacturing imperfections but also inherent wavefront contributions from the autoreflection testing setup. The magnitudes of the latter are affected by both the spherical substrate and the groove pattern. Through the analysis of geometric aberrations of spherical gratings, the groove pattern contributions are demonstrated to be contrary for the opposite diffraction orders. A nonnull interferometric testing of spherical gratings is proposed without foreknowledge of the groove pattern, in which the wavefront errors contributed only by the manufacturing imperfections are derived from dual measurements under Littrow conditions with opposite diffraction orders. Simulations are implemented for varied line spacing (VLS) spherical gratings with an F-number slower than 1.5 and groove density varying from 150 to 300 lp/mm, and the residual error less than 0.004 λ RMS is obtained. The residual misalignment error after conventionally removing defocus and tilt is further analyzed and discussed. A VLS grating in which the NA is 0.13 and groove density is 200 lp/mm is chosen as an experimental sample, and the diffracted wavefront error with 0.018λ RMS is obtained.

We present a compact dual-view endoscope imaging system with a field of view (FOV) of ±80° and F/# of 3.4. The endoscope consists of two optical configurations for increasing FOV within the volume constraint. The front view configuration is a fisheye lens with a FOV of ±55°, and the side view configuration is a panoramic annular lens that covers the remaining FOV. The two configurations are combined by a hybrid lens that consists of center refractive portion and side catadioptric portion. Both the front and rear surfaces of the hybrid lens are aspherized with the use of annularly stitched Q-type aspheres. Thus, a compact endoscope is successfully implemented with fewer lenses, with a total length of 11.5 mm and a maximum diameter of 5.5 mm. The modulation transfer function at 167 lp/mm is above 0.4 over the entire FOV. The relative illumination is more than 0.65 and the optical distortion is within 10%. Moreover, the near telecentric condition is fulfilled and supports constant magnification focusing.

We substitute a freeform surface consisting of the off-axis parabolic (OAP) surfaces for the collimating mirror and each sub-region of the focusing mirror, to achieve an aberration free spectrometer.

With the development of modern precision optical fabrication and measurement technologies, optical freeform surfaces have been widely employed in different applications, especially in off-axis refl...

We demonstrate a lensless phase-shifting point diffraction interferometer with a tiny pinhole to measure spherical mirror surface figures. The interferograms used to reconstruct the surface figure are formed without imaging optics. Fresnel diffraction calculations with a coordinate transformation are studied as a means of reconstruction method for wavefront amplitude and phase. The Radon transform is used to determine the distance from the tiny pinhole to the CCD target, which guarantees the accuracy of the diffraction calculations. Our lensless phase-shifting point diffraction interferometer not only retains the higher measurement precision by the ideal reference wavefront, but also overcome the fabrication and mounting limitation of the imaging optics. The simulations and experiments have validated the accuracy and feasibility of the spherical mirror measurement by proposed lensless phase-shifting point diffraction interferometer.

Dual-wavelength interferometry (DWI) could extend the measured range of each single-wavelength interferometry. The synchronization of the two working wavelengths in DWI is of high efficient, and the generated moire fringe indirectly represents the information of the measured long synthetic-wavelength (λS) phase. However, the extraction of the measured synthetic-wavelength phase is rather arduous from the moire fringe. To retrieve the synthetic-wavelength phase from the moire fringe patterns, we present a carrier squeezing dual-wavelength interferometry method (CSDI) in simultaneous DWI (SDWI). After the mathematical square of the moire fringe patterns, the multiplicative moire phase-shift fringe patterns with π/2 phase shift at λS are combined into a single spatial-temporal fringe (STF). By converting the temporal phase shift into spatial carrier and the introduction of the carrier, the measured synthetic wavelength phase is retrieved by the filter and inverse Fourier transform of the STF spectrum. Compared with other methods, CSDI method could suppress the influence of the phase-shift error and only requires 4 frame phase-shift interferograms. Numerical simulations are executed to demonstrate the performance of the CSDI method in SDWI with the peak-to-valley (PV) value of 1.46 nm and the root mean square (RMS) values of 0.23 nm for the demodulated error. And the precision is better than PV of 20 nm (0.0059λs) and RMS of 6 nm (0.0017λs) even when the distribution range of the phase-shift error is as high as ± 10% relative to the π/2 phase shift step at λS. Finally, our experimental results indicate that the measurement accuracy is better than 1.3% for a step with the height of 7.8 µm, and 0.5% for the step height of 6.233 µm for a Fresnel lens.

Tunable devices based on bilayer metasurfaces have attracted researchers’ attention in recent years for their accurate tuning abilities and high integration. In tunable devices such as tunable beam splitters and Alvarez metalenses, opposite quadratic or cubic target phase profiles are imparted on both layers, and a varying total phase profile arises through the relatively lateral displacement between the two layers. However, there is a lack of a generalized target phase profile design method to design these tunable devices. In this study, a generalized phase profile design method named Integral of Total Phase Profile Difference (ITPD) is proposed to calculate the target phase profiles of both layers. Multiple integral equations describe the relationship between the target phase profiles and the total phase profiles. Based on this method, a tunable beam splitter and an Alvarez metalens are redesigned respectively. Moreover, a new tunable device that can be converted from a beam splitter to a metalens is designed by the ITPD method. The ITPD design method is promising for designing tunable devices with arbitrary total phase profiles in dynamic or multifunctional optical systems.

White-light scanning interferometry is an effective and widely used technology for measuring the microscopic three-dimensional morphology of an object. Its vertical resolution can reach the sub-nanometer level, and its lateral resolution reaches submicron level. However, for the samples containing complex structure or high-density periodic distribution structural units, the measurement results are strongly restricted by magnification and numerical aperture (NA) of the microscopic objective. In this paper, we proposed a three-dimensional reconstruction algorithm for white-light interferograms after super resolution processing, using fast super-resolution convolutional neural networks (FSRCNN) to improve the detailed information of the interferograms, and then we used centroid method combined with the five-step phase-shift method to extract the zero optical path difference (ZOPD) position of the interference signal after super resolution processing. After processed by the proposed method, the interferograms collected by the 10X microscope objective (NA=0.3) recovered the 3D surface is the same as that measured by the 100X microscope objective (NA=0.7), which is proved by the experiment results.

Sparsely and randomly distributed internal defects in the optical component can cause an inferior signal quality and serious measurement errors. A modified three-dimensional extend ptychographic iterative engine (modified-3PIE), which splits a sample into axial sections with known positions, is proposed to evaluate and reconstruct internal defects. The axial positions of internal defects are calculated to reduce the number of axial sections. There are only several axial sections with defects that are located at the calculated positions, and other sections are free-propagation parts. The complex amplitude transmittances of internal defects at different axial section positions are simultaneously retrieved. Simulation and experiments are conducted to verify the performance of the proposed method. Our proposed method does not require a reference beam and imaging system, and it can be applied to reconstruct a large area of the sample.

Dual-wavelength interferometry could extend the measured range of single-wavelength interferometry by combining the two single wavelength phases, particularly for the measurement of step height. When testing the high-reflectivity surfaces with the single wavelength Fizeau interferometer, we have presented the π ∕ 4 phase-shift carrier squeezing interferometry (QCSI) method for phase extraction with multi-beam interference ( Appl. Opt . 55, 1920–1928, 2016). In this paper, we propose an integer and decimal portions synthetization (IDS) method for the multi-beam interference in the dual-wavelength Fizeau interferometer. One of the single wavelength wrapped phases is demodulated by the multi-beam interference QCSI algorithm, while the second of the single wavelength wrapped phases is extracted by the conventional two-beam interference phase-shift algorithm, so the equivalent wavelength unwrapped phase is derived from the two single wavelength wrapped phase. The decimal portion of synthesized phase is then obtained directly from the first single wavelength wrapped phase, and the integer portion of synthesized phase is obtained from the fringe order of the first single wavelength wrapped phase determined by the equivalent wavelength unwrapped phase. The proposed non-iterative IDS method avoids the common error magnification effect in the two-wavelength techniques, and only requires no more than 8 frame phase-shift interferograms for each single wavelength. Its robust performance is validated by both simulations and experiments in the presence of multi-beam interference as well as phase-shift error for measuring objects with height discontinuities.

We present the optical design of a Czerny-Turner imaging spectrometer for which astigmatism is corrected using off-the-shelf optics resulting in spectral resolution of 0.1 nm. The classic Czerny-Turner imaging spectrometer, consisting of a plane grating, two spherical mirrors, and a sensor with 10-μm pixels, was used as the benchmark. We comparatively assessed three configurations of the spectrometer that corrected astigmatism with divergent illumination of the grating, by adding a cylindrical lens, or by adding a cylindrical mirror. When configured with the added cylindrical lens, the imaging spectrometer with a point field of view (FOV) and a linear sensor achieved diffraction-limited performance over a broadband width of 400 nm centered at 800 nm, while the maximum allowable bandwidth was only 200 nm for the other two configurations. When configured with the added cylindrical mirror, the imaging spectrometer with a one-dimensional field of view (1D FOV) and an area sensor showed its superiority on imaging quality, spectral nonlinearity, as well as keystone over 100 nm bandwidth and 10 mm spatial extent along the entrance slit.

We report an automated differentiation model for classifying malignant tumor, fibro-adipose, and stroma in human breast tissues based on polarization-sensitive optical coherence tomography (PS-OCT). A total of 720 PS-OCT images from 72 sites of 41 patients with H&E histology-confirmed diagnoses as the gold standard were employed in this study. The differentiation model is trained by the features extracted from both one standard OCT-based metric (i.e., intensity) and four PS-OCT-based metrics (i.e., phase difference between two channels (PD), phase retardation (PR), local phase retardation (LPR), and degree of polarization uniformity (DOPU)). Further optimized by forward searching and validated by leave-one-site-out-cross-validation (LOSOCV) method, the best feature subset was acquired with the highest overall accuracy of 93.5% for the model. Furthermore, to show the superiority of our differentiation model based on PS-OCT images over standard OCT images, the best model trained by intensity-only features (usually obtained by standard OCT systems) was also obtained with an overall accuracy of 82.9%, demonstrating the significance of the polarization information in breast tissue differentiation. The high performance of our differentiation model suggests the potential of using PS-OCT for intraoperative human breast tissue differentiation during the surgical resection of breast cancer.

Dielectric metasurfaces, which are capable of manipulating incident light, have been a novel branch of flat optics. This modulation ability is realized by nanostructures with space-variant geometrical parameters such as height and diameter. Therefore, accurate profile measurement of metasurfaces is of great importance. White-light scanning interferometry is widely used for profile measurement. The step height is retrieved by locating the envelope’s peak. However, spurious fringes attached to the desired fringes were observed at the measured area near the edge of nanostructures. Their amplitude distributions vary with the density of nanostructures as well as distance to the edge. Further, anomalous coherence signals with two fringe envelopes are produced, which result in inaccurate measurement results. We attributed this phenomenon to the complex light modulation by the nanostructures. When referring to the anomalous coherence signals for the top of the nanostructures, one envelope is produced by the top, and the other is produced by the bottom; however, it is difficult to distinguish these two, which is the same case for the bottom of the nanostructures. To automatically solve these obstacles, a signal processing method, which integrates the image segmentation technology to identify and divide the anomalous coherence signals, along with a Morlet wavelet transform to extract the fringe envelope, suitable for any measured area of the dielectric metasurface, is proposed. One metasurface belt consisting of seven kinds of nanopillars with varying arrayed densities that produce different coherence signals is measured. The diameter distribution ranges from 500 to 1250 nm with a constant height of 1850 nm. The local periods in the X and Y directions are 3020 and 1740 nm, respectively. Measurement results demonstrate the validity of the proposed method for spurious fringes processing.

In this paper, a direct design method for an off-axis two-mirror telecentric scanning system with a linear field of view (FOV) is proposed. A single freeform mirror structure is firstly considered, in which the aberration free geometry of the off-axis parabolic (OAP) surface is leveraged to provide the focusing function and build surface contour of the sub-region on the mirror for each FOV. Multiple OAP surfaces for construction of the freeform mirror are located at an OAP base to satisfy the telecentric condition. The imaging distortion of this single freeform mirror structure is analyzed and found unavoidable due to the unsymmetrical geometry of the OAP base. A freeform reflective corrector is supplemented, and it is constructed from multiple plane surfaces located at a curved base to fulfill the f-theta scanning geometry. Thus, a two-mirror structure composed of one freeform primary mirror and one freeform reflective corrector is established. Each plane-OAP surfaces pair corresponds to a specific FOV. These multiple OAP surfaces and multiple plane surfaces are then expanded and mixed respectively, to construct the freeform primary mirror and freeform reflective corrector. An f-theta two-mirror freeform scanning system with ± 10.4° linear FOV is designed using the proposed construction method. The design result is diffraction-limited, and a scanning error less than 5 μm and telecentricity angle less than 0.2° are achieved.

Subaperture stitching interferometry (SAS) is an important method for map testing of large aperture optical components, in which a mechanical structure is often employed for the testing of each subaperture. By eliminating the phase deviation of the corresponding points in the overlapping regions of every adjacent subaperture, the whole aperture map can be obtained. Accurate subaperture positioning is an important guarantee for precise stitching. In this paper, a hybrid optimization algorithm is proposed to realize subpixel-level positioning accuracy in SAS based on the combination of the phase correlation and iterative gradient methods. The phase correlation method is adopted to calculate the pixel-level positioning deviation first, and the subpixel deviation is derived and then corrected by iterative optimization through the gradient method. The subpixel-level positioning accuracy of the proposed optimization algorithm is verified by simulations and a 76.2 mm off-axis parabolic mirror is chosen as an experimental testing sample. The surface map obtained from the proposed hybrid optimization method is consistent with the full aperture testing result, which also verifies that the proposed optimization algorithm is a powerful tool with subpixel-level positioning accuracy in SAS testing.

White-light scanning interferometry is an effective and widely used technology for measuring the microscopic three-dimensional morphology of an object. However, it is easily affected by external disturbances and appears to have a non-uniform sampling problem, which reduces the measurement accuracy. In this study, an effective correction algorithm is presented, in which a Hilbert transform and a correlation analysis of the white light interference envelope curves, as well as the simulated ideal interference signal envelope, are employed for a robust and high precision signal correction. In addition, the proposed method is at least 4 times as accurate as a traditional method and achieves a high repeatability, which is analyzed through a simulation and contrast experiments.

The ideal mapping geometry in a Fizeau interferometer is to map equal height increments on a flat object and equal angle increments on a spherical surface to equal heights on the detector. So the initial intent of the optical design of Fizeau transmission spheres (TSs) is to provide R‐θ mapping geometry for equal angle increments. The corresponding unequal heights mapping will introduce retrace error as coma when linear carrier fringes exist. On the contrary, equal heights mapping with R‐sin θ mapping geometry will avoid linear carrier fringes induced coma error. These two different mapping geometries conflict especially for the TS with a small f-number. In this paper, we will first explore the design and the performance of the f/0.75 TS according to the two different mapping geometries, and then evaluate the mapping geometry for the commercial ZYGO f/0.75 TS, and give some engineering notes for the designers, the metrologists, and the fabricators in the optical laboratory.

Light projection function is a major area of interest within the field of designing ultra-wide angle cameras. In this paper, we introduce a novel ultra-wide angle projection function that is characterized by an angle-variant distortion model similar to that of human retina space-variant resolution. The projection peculiarities were compared with the classical equidistant fisheye projection function to illustrate the benefits of our projection model on real-time tracking and ultra-wide angle imaging applications. The new projection model produced an accurate result with uncomplicated distortion control using Zemax user-defined macro program. The inverted model is also successfully used in correcting such distorted image. The paper shows as well the design of an original 170° fast foveated fisheye lens that provides more than 52 % undistorted image with a high-resolution performance over the entire lens field of view.

We propose a high-order shift-rotation absolute ultra-precision measurement method to calibrate the misalignment aberration and reference surface deviation in high-numerical-aperture spherical surface testing. Based on high-order approximation, the high-order misalignment aberrations are deduced. Both the computer simulation and experimental results confirm the feasibility of the proposed absolute ultra-precision measurement method. The high-order misalignment aberrations and reference surface deviation can be removed from the measured results by our absolute measurement method. The high-order shift-rotation absolute measurement method can get the accuracy of nanometer level in high-numerical-aperture spherical surface testing.

Misalignment aberrations in Fizeau interferometric testing system can significantly influence the measurement results in the case of high-numerical-aperture test spherical surfaces, and it is hard to separate the high-order misalignment aberrations from the measured data. The traditional calibration method, which is based on linear-approximation, is applicable in calibrating only the linear misalignment aberration in measurement of high-numerical-aperture spherical surfaces. Based on modified power term for interferometry and 4-overlapping averaging 9-frame algorithm, sub-nanometer accuracy high-order calibration method is proposed to calibrate the linear misalignment aberrations as well as high-order misalignment aberrations. Both the computer simulation and experimental results confirm the feasibility and accuracy of the proposed calibration technique, and sub-nanometer misalignment aberrations can be calibrated. The proposed method can also used in spherical surface ultra-precision measurement by other interferometric setups without foreknowledge of numerical aperture of the test surface.

A simplified and compact F/2.8 fisheye lens system comprising only 6 lens elements with just one aspheric surface was successfully designed. 160° full field of view, and 11.6 mm lens total tracking length were intended. We further described the ultra-wide angle lens system design challenges and their overcome problems. Our lens system performance evaluation was done by ZEMAX optical design software. A perfect lateral color and axial chromatic aberration correction were achieved, and the relative illumination is above 85 % across the entire field of view with an admirable corrected field curvature along with fθ distortion less than 0.15 %. Our lens modulation transfer function produces a high-resolution projection with brightness uniformity for endoscopic, security, and monitoring applications.

The pupil scanning modulation is a maneuverable method for retrieving the phase of the complex-valued object. It is based on changing the extent of the illumination function using an adaptive aperture. The apertures are fixed on the same border or point of intersection that ensures the location of the aperture. We sequentially increase the size of the aperture and guarantee the necessary overlap between adjacent object fields. An improved algorithm including the adaptive raised-power estimation constraint and gradient-descent step is proposed to accelerate convergence and avoid stagnation during iterations. Both the simulation and experiment have been conducted to verify the feasibility of this method.

The conjugate differential method has been applied to the absolute test of flat, cylindrical, and axicon surfaces. In the previous work, simulations and correspond experiments have been carried out to verify the feasibility of the method. To analyze the influences of different factors upon the measurement result, the conjugate differential method is discussed in detail. Considering the characteristics of the test surface such as surface types and surface profiles, the application ranges of the conjugate differential method are discussed into three parts. According to the three surface types using the conjugate differential method, the method can be extended to the absolute test of the spherical surfaces based on spherical coordinate system. The reconstructed errors caused by different aberrations expressed as Zernike polynomial terms show that they are more sensitive to high order aberration terms of the surface under test. And for surfaces with different frequency distributions, the surface with less mid-spatial frequency information is less sensitive to the sampling frequency. The influence from the other factors in interferometric test are also discussed into three parts. The influences from the uncertainty of shifts are correlated with the increased aperture diameters, since the integration error caused by the shift error increases gradually with the expanding of the integration path. The integration error changes by the influences from the coherent noise and pixel noise related to pixel deviations. The reconstructed deviations get increased while the peak pixel deviation is increasing. For the balance of the differential deviation and integration error, the optimization of sampling resolution should take considered for accuracy improvement.

Multilayer defects which reside on the top or inside the multilayer are one of the most critical concerns in the extreme ultraviolet lithography (EUVL) manufacturing process. We proposed the transport of intensity equation and partial least-square regression (TIE & PLSR) method to inspect the defect and reconstruct its geometric parameters: height and full width at half maximum (FWHM). The transport of intensity equation (TIE) is employed to retrieve the phase of the multilayer defect from the two scattering images, which collected at two adjacent propagation distances. Comparing the simulated ideal phase, the phase deformations caused by different top heights and widths of the defects are analyzed. The optical properties maximum, minimum and fitting Zernike coefficients are used to parameterize the phase deformation. Partial least-squares regression (PLSR) is applied to associate the optical properties of the phase deformation with the geometric parameters of the defects, and reconstruct geometric parameters of the measured defect from the established data library. The reconstruction error is less than 0.2% in simulation experiment.

Optical window is a multifunction window. It is not only a window that let the light come through, it is also a window, which isolate the vacuum environment inside the bottle from the outside atmosphere environment. At the same time, it is as well as a temperature-controlling window that can separate the heat sink inside the bottle away from the outside normal temperature. The thickness of the glass should be large enough to guarantee the strength and reliability of the window. But if the window glass is too thick, it would lead to the temperature change and, furthermore, would cause to the change of refractive index gradient and also, the thermal deformation will be more apparent. It may even be able to meet the requirements of the optical indicator when the situation gets worse. Based on the thermal optical analysis, with one side in normal pressure, and the other in 1 × 10−3 Pa vacuum, 100 K degrees, the thickness of the silica glass and the germanium optical window is optimized. The thermal environment of optical window is analyzed, including system average temperature shift as well as circumferential, radial and axial temperature differences. By calculate the result of steady state temperature field and mapping it to structural model, the deformation of optical window under the force-thermal coupling condition could be figured out. The thermal optical analysis could also be carried out after combining refractive index gradient analysis and glass surface change of optical window. With the differences of glass thickness, the optical path in root mean square error (RMS) of silica glass optical window with diameter of 230 mm and the germanium optical window with diameter of 150 mm is calculated. The results show that the optical window can not only meet the strength and reliability requirements, but also meet the optic index in the effective optical aperture. These results provide the guidance for the optical window design.

A method for measuring the radius of curvature with a pinhole point diffraction interferometer (PDI) is proposed. Using the wavefront difference method and the Gaussian imaging equation, the longitudinal displacement of the converging rays passing through a standard plane-parallel-plate sample in PDI interference cavity is determined. Based on this longitudinal displacement, a precise formula for radius of curvature calculation is deduced. An experimental system for radius of curvature measurements is set up to verify the principle. With this testing system, the radius of curvature of spherical mirrors and the surface figure can be measured in a higher precision simultaneously. Some sources of uncertainty in measurement are discussed based on detailed error analysis. The experimental results indicate that the measurement accuracy Δ R / R 0 is in the order of 10−4.

The surfaces and refractive index of crystalline lens play an important role in the optical performance of human eye. On the basis of two eye models, which are widely applied at present, the effect of lens surfaces and its refractive index distribution on optical imaging is analyzed with the optical design software ZEMAX (Zemax Development Co., San Diego, USA). The result shows that good image quality can be provided by the aspheric lens surfaces or (and) the gradient-index (GRIN) distribution. It has great potential in the design of intraocular lens (IOL). The eye models with an intraocular implantation are presented.

We present a compact dual-view endoscope objective lens with a field of view (FOV) of ± 80°and F/# of 3.4. The endoscope consists of two optical configurations for increasing FOV within the volume constraint. The front view configuration is a fisheye lens with a FOV of ± 55°, and the side view configuration is a panoramic annular lens that covers the remaining FOV. The two configurations are combined by a hybrid lens that consists of center refractive portion and side catadioptric portion. Both the front and rear surfaces of the hybrid lens are aspherized with the use of annularly stitched Q-type aspheres. Thus, a compact endoscope is successfully implemented with fewer lenses, with a total length of 11.5 mm and a maximum diameter of 5.5 mm. The modulation transfer function at 167 lp/mm is above 0.4 over the entire FOV. The relative illumination is more than 0.65 and the optical distortion is within 10%. Moreover, the near telecentric condition is fulfilled and supports constant magnification focusing.

The classic Czerny-Turner spectrometer consists of a plane grating and two spherical mirrors. The optical path geometry adopted for incident and grating dispersed light is off-axis reflection, so the spherical collimating and focusing mirrors introduce coma and astigmatism. The conventional configuration is asymmetrical for coma automatic compensation, but suffers from astigmatism. We substitute the off-axis parabolic (OAP) surfaces for spherical surfaces of the collimating mirror and each sub-region of the focusing mirror, to achieve an aberration free configuration. The multiple OAP surfaces are then expanded and mixed, to construct a freeform surface integrating the collimating and focusing mirrors into a single element. Results show that a 0.1 nm spectral resolution is achieved over a bandwidth of 400 nm centered at 800 nm, in the designed spectrometer comprised of a plane grating and one freeform mirror. The construction method is advantageous to integrated optic design, and the resulting freeform mirror spectrometer is compact, and simplifies manufacture and alignment.

The aberrated wavefront propagates along its normal. Both the magnitude and boundary change after the propagation. Wavefronts characterized by Zernike coefficients and a normalized pupil radius can also be represented by a bundle of feature rays normal to the local surface. A ray transfer matrix parameterized by the pupil radius and propagation distance is proposed to transfer these feature rays to obtain the slope and position data of the propagated feature rays. Numerical orthogonal Zernike gradient polynomials are derived to reconstruct the wavefront from the discrete data by using a numerical method. Two aberrated wavefronts are performed as examples to validate the accuracy and flexibility of the proposed numerical method.

The precision single point diamond turning technique has been a promising technology for generating small and medium-sized freeform optical elements with high surface quality. In this paper, we present an extremely off-axis freeform optical system with a large 10.0 mm pupil diameter and a low 3.0 F-number over a wide 28° field of view. It is composed of two freeform aluminum mirrors, which are fabricated efficiently by the single point diamond turning machine. The manufacturing strategy and parameters are estimated rationally and comprehensively, based on the freeform surface characters. The freeform aluminum mirror surface can reach submicron surface accuracy and achieve nanometer surface roughness. The final assembled prototype of the off-axis two-mirror freeform display optical system has the advantages of compactness, a broad spectrum, and good display imaging performance.

A Fizeau infrared interferometer designed and built with a broadband wavelength channel ranging from mid-wave infrared to long-wave infrared is described. The exchange of working wavelengths from 4.41 μm to 10.6 μm is provided because the elements making up the optical paths are reflectors or beam splitters, together with the relay lenses and imaging lens for chromatic aberrations correction, which also realize the reimaging technique to permit the high cold stop efficiency. An elaborate dual-triangle optical path design is applied to share one detector for both alignment and view. On the premise of online calibration of the piezoelectric transducer, π /4 phase-shifting averaging technique is applied for compensation of ripple error introduced by multi-beam interference due to high reflectivity of infrared test optics, with simulative and experimental validation. Besides, considering the small field of view of the off-axis parabolic mirror as the beam collimator, the restrictions of misalignment indicated by carrier fringes are given through model of ray tracing, which guarantees the performance of the infrared interferometer with accuracy better than PV 0.05 λ and rms 0.01 λ .

Freeform optical surfaces (FOSs) will be the best elements in the design of compact optical systems in the future. However, it is extremely difficult to measure freeform surface with sufficient accuracy, which impedes the development of the freeform surface. The design and fabrication of computer-generated hologram (CGH), which has been successfully applied to the tests for aspheric surfaces, cannot be directly adopted to test FOSs due to their non-rotational asymmetry. A novel ray tracing planning method combined with successively optimizing even and odd power coefficients of phase polynomials in turn is proposed, which can successfully design a non-rotational asymmetry CGH for the tests of FOSs with an F-θ lens. A new eight-step fabrication process is also presented aiming to solve the problem that the linewidth on the same circle of the CGH for testing freeform surface is not uniform. This problem cannot be solved in the original procedure of CGH fabrication. The test results of the step profiler show that the CGH fabricated in the new procedure meets the requirements.

This letter shows that the human eye fundus tissue has higher reflectivity at the near-infrared (NIR) wavelength, and that some aberrations exist at the pre-optical system from cornea to vitreous. We design a NIR fundus camera with inner focusing, which can be applied to the -10 D to 10 D range of vision and has the advantage of ensuring the stability of image when is focused. Considered as Liou's eye aberration model, we correct the integrated aberration to ensure a 100 lp/mm resolution when we complete the assembly and calibration of the fundus camera. Kohler illumination is also applied to obtain uniform fundus illumination. Moreover, we put forward a novel method for stray light elimination based on polarization switch, which inhibits ghost image formation near the focal plane when the illumination beam is reflected by the eyepiece surface. The result shows that this method is effective in ensuring an illumination uniformity of 80%, with the advantage of simple structure and easy assembly.