The projection model regulates the mapping relationship between the object and image for the imaging system, where they are related by the focal length. The distortion is defined as the departure from the similarity between the object and image, or the departure from the targeted projection model. Thus, the focal length and distortion represent the actual relationship of the optical system. The focal length is the most important and basic parameter of an optical system, which is theoretically defined utilizing the" minor aperture method". According to the regulation of" minor aperture method", the ray close and parallel to the optical axis is traced, and then its angle of convergence after passing through the optical system is recorded for focal length calculation. This regulation is easy to execute during the optical design process but hard to execute for the measurement of the built performance of the optical system. The" minor image height method"is the frequently adopted regulation for focal length measurement, in which ray with minor field of view is traced, and the corresponding image height is recorded for focal length calculation. The" minor image height method" is easy to execute for both design and measurement, and aligns well with the definition of projection. Therefore, if the definition of the focal length is developed from the on axis field of view to the off-axis field of views, then the local focal length which is a field dependent parameter is involuntary generated. And the" minor image height method"is adopted for local focal length definition, in which the image height increment for a minor angle increment is regulated for each field of view. Moreover, the distortion is represented by the variable local focal length for different field of views. And then, the local focal length can be adopted in the process of optical system design for distortion control, for its calculation in the design coincides well with the measurement in the experiment, which is the outstanding priority according to its regulation. A fisheye lens with field of view of 160 degrees, F-number of 4.2, on focal length of 1.61 mm is firstly designed utilizing the local focal lengths for 11 sampled field of views as the target. It is composed of 6 pieces of lenses,in which one aspherical surface is set at a plastic lens,and the equidistant projection is fulfilled. Inspired by the foveated fisheye, the theory of high resolution with rectilinear projection in the central field of view is proposed,and the aforementioned fisheye lens is successfully transformed to the configuration with equidistant projection for the 50% central field of views,adopting the local focal length as the optimization target. Other than objects in the infinity,there are some cases in which the objects is imaged from finite distance,and the object is sometimes even curved. The wide angle lenses with field of view of 120 degrees,F-number of 2.8,on focal length of 1mm are then designed still utilizing the local focal length as the optimization target. The curved objects are 1 000 mm away from the lenses,with the radius of curvature of 800,1 000,1 200,- 20 000 mm and infinity,corresponding to convex spherical objects,concave spherical object and plane object respectively. The target local focal length is derived according to the imaging purpose for equal resolution on the curved objects. Diffraction limited imaging quality is achieved,and local focal length relative error is constrained to less than 0.6% with 11 sampled field of views,and the distortion is then less than 0.21%. The generation of local focal length provide a novel parameter for optical system design with complex projections,leveraging its priority of design and measurement coincidence.

Topographic spatial resolution is a metrological characteristic that describes the ability of a surface topography measuring instrument to distinguish closely spaced surface features. The optical and the topographic spatial resolutions are intuitively correlative for coherence scanning interferometry (CSI), and the latter is larger than the former. This paper aims to develop a model to study their relationships, and pursue the topographic spatial resolution improvement through pupil modulation. First, we construct a comprehensive Fourier model for CSI with the grating taken as the typical sample under test, in which the effect of pupil modulation is also considered. Second, the model is employed to generate the interference signal at the sampling point either away from or close to the edge of the grating adopting the pupil modulation. Then the scheme of the topographic spatial resolution enhancement by pupil modulation is investigated. Third, the topographic spatial resolution of the grating is quantified using the small scale fidelity limit, which is explained and defined based on the proposed threshold determined by both period and height. Using the RS-N resolution standard and the Siemens star as measurement samples, and adopting the obscuration ratio as 0.5 with optical pupil modulation, we demonstrate that optical resolution is enhanced by 20%, leading an improvement in topographic spatial resolution by 20% as well, which is in good agreement with the predictions deduced from the model.

Coherence scanning interferometry (CSI) is a widely used non-contact method for measuring areal surface topography. The calculation of groove depth typically employs the ‘W/3 rule’ specified in ISO 5436-1. However, the batwing effect causes overshoots near the groove edges, which can introduce noise singularities in the selected W/3 region for depth calculation, thereby affecting the measurement of rectangular grating depth. This paper introduces the definition of batwing height and width and proposes a simulation model that considers various factors, such as the center wavelength, spectrum of the illuminating light, shadow effect, and numerical aperture, to analyze their influence on depth measurement. The simulation results demonstrate that the batwing width is the primary factor influencing depth measurement for small grating periods. Specifically, a decrease in numerical aperture increases the batwing width, leading to larger depth measurement errors, while a decrease in the center wavelength reduces the batwing width, resulting in smaller depth measurement errors. The influence of the illumination spectrum and shadow effect on depth measurement is found to be minor. Experimental validation using a step standard consisting of rectangular gratings with different periods and depths confirms the agreement between the experimental and simulated results. The proposed method provides a quantitative evaluation of depth measurement accuracy in CSI.

Objective White light interferometry, as an effective non-destructive method, is widely employed for measuring characteristic parameters of microstructures. Among these microstructures, the rectangular grating is a typical periodic step structure and has extensive utilization in precision machining due to its diverse materialization properties based on surface morphology characteristic parameters. However, when the groove depth of the grating is smaller than the coherence length of the adopted light source, the batwing effect occurs near or at the edge of the step in the sample under measurement. ISO series 25178 provides a standard morphology for calculating the characteristic parameters of groove depth and linewidth through three-dimensional surface morphology analysis, which necessitates determining the position of the step edge. The batwing effect poses challenges to precisely locating the step edge position and may result in a false representation of information near the edge of the step discontinuity. We propose a new algorithm for determining the characteristic parameters of rectangular gratings by utilizing the distribution difference of the coherence signals between the upper and lower surfaces, thus avoiding the traditional method of extracting step edge position from three-dimensional surface morphology. The introduced algorithm demonstrates excellent measurement accuracy, high repeatability, and exceptional robustness in calculating the desired characteristic parameters of rectangular gratings. Methods We propose an algorithm for precise positioning of the step edge in rectangular gratings based on the distribution difference of the coherence peak among different sampling points. The algorithm is designed to improve the detection efficiency of characteristic parameters by incorporating parallel processing techniques. Firstly, during vertical scanning, the coherence signals undergo modulation. Simultaneously, the contrast information is obtained by the gravity method to extract the center of gravity position of the modulation envelope across all sampling points within the field of view. Then, the peak of the contrast envelope is calculated to further accentuate the discrepancy between the upper and lower surfaces of the rectangular grating. By identifying these surfaces, we acquire the step position information, which allows to generate the mask matrix and determine the linewidth values. To obtain the groove depth, we combine the mask matrix and three- dimensional surface morphology of the rectangular grating. Meanwhile, we extend the application of the "W/3" guideline specifically for the rectangular grating structure to mitigate the influence of the batwing effect on depth measurements. Additionally, we incorporate the Stoilov algorithm to calculate the contrast information during the vertical scanning, enabling simultaneous determination of the step edge position and three-dimensional surface morphology. This parallel processing approach enhances the efficiency and accuracy of the algorithm. Generally, our algorithm provides an effective means for precisely positioning the step edge in rectangular gratings, while considering the influence of the batwing effect on depth measurements. Results and Discussions Experiments are conducted via a self- developed white light interferometry system to evaluate the feasibility and accuracy of the proposed method. Two rectangular gratings with different characteristic parameters are selected as measurement samples. The first sample calibrated by Physikalisch- Technische Bundesanstalt (PTB) has a groove depth of 189. 6 nm +/- 1. 0 nm and a linewidth of 6 mu m. The second sample certified by VLSI standards traceable to the National Institute of Standards and Technology ( NIST) has a groove depth of 90. 5 nm +/- 2. 8 nm and a linewidth of 50 mu m. Ten repeatability measurements are performed in the same area of each sample based on the proposed algorithm. For the first sample, the average depth value is determined to be 188. 97 nm with a relative error of 0. 33% [Fig. 8( a)]. The average linewidth value is measured to be 6. 12 mu m with a relative error of 2% [Fig. 8( b)]. Similarly, for the second sample, the average depth value is 90. 10 nm with a relative error of 0. 40% [ Fig. 8(c)]. The average linewidth value is determined to be 99. 04 mu m with a relative error of 0. 96% [Fig. 8(d)]. These measurement results demonstrate the accuracy and effectiveness of the algorithm. Furthermore, the standard deviation of the ten repeatability measurement results is analyzed to assess the algorithm stability. The small standard deviation confirms the consistent and reliable performance of the proposed method. Additionally, the influence of error terms during the experiment on the measurement results is investigated. Specifically, variations in sample placement tilt angle, interference fringe numbers, and interference fringe direction are examined. The results indicate that these error terms exert minimal effect on the measurements, highlighting the robustness of the proposed algorithm. In general, the experimental results validate the feasibility and accuracy of the algorithm in accurately determining the groove depth and linewidth of rectangular gratings. The algorithm exhibits stability and robustness and becomes a reliable tool for precise metrology in surface morphology measurements. Conclusions We present a new approach for accurately measuring the characteristic parameters of rectangular gratings under the batwing effect. Unlike conventional calibration methods, our method focuses on the distribution difference of coherence signals between the upper and lower surfaces of the grating. This approach addresses the limitations of ISO series 25178 in accurately measuring the characteristic parameters in the presence of the batwing effect. To validate this method, we conduct simulations of interferograms during the vertical scanning based on linear system theory. By analyzing the modulation envelope of these interferograms, we can precisely detect the step edge position and distinguish the upper and lower surfaces of the grating sample. Finally, by applying ISO standards, we accurately measure the characteristic parameters of the rectangular grating. Experimental results using two rectangular gratings with different groove depths and linewidths demonstrate the repeatability and robustness of our method. The implementation of the "W/3" guideline in measuring rectangular gratings is significantly improved to accurately measure the characteristic parameters. Importantly, our method features high efficiency, high precision, and fine repeatability without requiring any physical upgrades to the instrument. Considering the ongoing trend towards miniaturization of rectangular gratings, our method has broader applications.

自由曲面设计自由度多、面型表征能力强等优势使成像光学系统突破了传统面型表征和系统结构的限制,在进一步提高成像质量的同时可以实现大视场、大孔径、小型化、轻量化等设计目标.良好的初始结构可以充分发挥自由曲面对像差的校正能力,提高系统设计效率.与共轴光学系统相比,自由曲面成像光学系统设计存在可参考样例少、像差理论尚不完善等问题,其初始结构的构造与求解仍然是先进光学设计领域的前沿热点问题之一.结合课题组多年的研究心得,探讨了现有的自由曲面成像光学系统初始结构设计方法,依据自由曲面构造原理将其分为同轴系统离轴化法、直接设计法、视场孔径扩展法和分段拼接融合设计方法,并分别介绍其设计原理和思路.最后对自由曲面成像光学系统初始结构设计中亟待解决的问题进行了分析总结.

Objective Given the increased prevalence of digestive diseases in recent years, the endoscope has been widely used for abdominal diagnoses, including those related to the stomach and intestines. Researchers are working to develop more effective and less invasive techniques for patients to benefit from endoscopy. A large field-of-view (FOV) and high resolution will reduce examination time and improve evaluation accuracy. Moreover, a compact endoscope structure is critical for minimising patient discomfort. In conventional wide-field camera lenses, a large panoramic scene needs to be focused onto an image sensor plane, to reduce the field curvature caused by the strong mismatch between the focal planes. The concentric lens consists of four refractive surfaces, and the centres of curvature of each refractive surface coincide at one point. Therefore, off-axis aberration does not exist. Only spherical and axial chromatic aberrations need to be corrected. Therefore, this structure can be applied to optical systems with miniaturisation, high image quality, and a large FOV; however, the image surface formed by the concentric system is curved. In this study, we correct the curvature of the field in the concentric sphere system by designing an annularly stitched aspheric surface to achieve flat-field imaging with a large FOV. Methods In this study, an optical system with full FOV is regarded as a combination of multiple single- or small-FOV sub-system units, then the sub-field units are solved separately, and the formation of a complete complex surface is optimised to realize the construction of a complete optical system. First, the initial concentric structure is solved with well-corrected spherical and chromatic aberration. Then, based on the FOV, an annularly stitched surface is constructed by dividing the surface into rings and calculating the initial structure parameters of each zone based on the flat-field conditions. The Q-type aspheric surface characterises different annuli to ensure imaging quality while obtaining good splicing results. Simultaneously, the continuity constraint condition of the annularly stitched aspheric surface is derived. Finally, a complete surface is optimized to realize the construction of a complete electronic endoscope. Results and Discussions The deviation of normal and sag between adjacent rings has been reduced to less than one-tenth of the test wavelength (typically test wavelength 632. 8 nm) through optimisation. These rings are then fused after the optimisation. The system diagram is shown in Fig. 10. Compared with the modulation transfer function (MTF) curve of the initial structure in Fig. 3, the MTF of the system after optimisation is more than 0.3 at the spatial frequency of 72 lp/mm (Fig. 11). Thus, the curvature of the full FOV is reduced from 0. 5 mm in the initial structure to within 0. 1 mm [Fig. 12 (a)] , the imaging requirements of electronic endoscope objectives are met. To validate the design results' manufacturability, a Monte Carlo simulation analysis was performed 200 times within the tolerance range (Fig. 14) . Consequently, in the full FOV, considering mass production and assembly, a probability that an optical system with an average diffraction MTF greater than 0. 3 at 72 lp/mm frequency can be obtained is more than 90%. Conclusions Based on the concentric structure, multiple rings are superimposed on the last surface to obtain different optical powers to generate the initial surface shape of the splicing surface of the rings. The surface shapes of the multiple rings are fused to generate a complete continuous surface after the continuous conditions are optimized. In the design, the Q-type aspheric surface is used to characterise different ring zones to ensure imaging quality. An electronic endoscope objective lens operating in the visible band is designed using this method. The objective comprises only four refractive surfaces, with a total system length of 2. 81 mm and FOV of 90 degrees. The field curvature of the system is less than 0.1 mm, the distortion is within 20%, the MTF reaches 0.3 at 72 lp/mm, and the relative illuminance of the full FOV is greater than 0. 5, which meets the imaging requirements of electronic endoscope objectives. The system uses the imaging advantages of the concentric objective lens with a large FOV and small volume. The annularly stitched aspheric surface is used to correct the curvature of the field caused by the spherical lens. Compared with the traditional structure, our electronic endoscope objective lens is more compact and readily manufacturable.

Y We present a compact dual-view endoscope imaging system with a field of view (FOV) of +/- 80 degrees 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 degrees, 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.

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.

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.

Journal of Cutaneous PathologyVolume 46, Issue 10 p. 798-799 BRIEF COMMUNICATION Excision recommendation rates of atypical (dysplastic) nevi amongst experienced dermatopathologists Euphemia W. Mu MD, Euphemia W. Mu MD orcid.org/0000-0001-5116-4126 The Ronald O. Perelman Department of Dermatology, New York University School of Medicine, New York, New York Piedmont Plastic Surgery & Dermatology, Charlotte, North CarolinaSearch for more papers by this authorLu Chen MD, Lu Chen MD orcid.org/0000-0002-8107-9720 The Ronald O. Perelman Department of Dermatology, New York University School of Medicine, New York, New YorkSearch for more papers by this authorLisa Rothman MD, Lisa Rothman MD The Ronald O. Perelman Department of Dermatology, New York University School of Medicine, New York, New YorkSearch for more papers by this authorBelen Rubio-Gonzalez MD, Belen Rubio-Gonzalez MD Pathology Department, University of California San Francisco, San Francisco, CaliforniaSearch for more papers by this authorEtan Marks DO, Etan Marks DO UT Southwestern/Cockerell Dermatopathology, Dallas, TexasSearch for more papers by this authorLeah Persad DO, Leah Persad DO UT Southwestern/Cockerell Dermatopathology, Dallas, TexasSearch for more papers by this authorClay J. Cockerell MD, MBA, Clay J. Cockerell MD, MBA UT Southwestern/Cockerell Dermatopathology, Dallas, TexasSearch for more papers by this authorPhil Leboit MD, Phil Leboit MD Pathology Department, University of California San Francisco, San Francisco, CaliforniaSearch for more papers by this authorShane A. Meehan MD, Corresponding Author Shane A. Meehan MD shane.meehan@nyumc.org The Ronald O. Perelman Department of Dermatology, New York University School of Medicine, New York, New York Correspondence Shane A. Meehan, MD, The Ronald O. Perelman Department of Dermatology, New York University School of Medicine, New York, New York 240 E. 38th Street, 11th Floor, New York, NY 10016. Email: shane.meehan@nyumc.orgSearch for more papers by this author Euphemia W. Mu MD, Euphemia W. Mu MD orcid.org/0000-0001-5116-4126 The Ronald O. Perelman Department of Dermatology, New York University School of Medicine, New York, New York Piedmont Plastic Surgery & Dermatology, Charlotte, North CarolinaSearch for more papers by this authorLu Chen MD, Lu Chen MD orcid.org/0000-0002-8107-9720 The Ronald O. Perelman Department of Dermatology, New York University School of Medicine, New York, New YorkSearch for more papers by this authorLisa Rothman MD, Lisa Rothman MD The Ronald O. Perelman Department of Dermatology, New York University School of Medicine, New York, New YorkSearch for more papers by this authorBelen Rubio-Gonzalez MD, Belen Rubio-Gonzalez MD Pathology Department, University of California San Francisco, San Francisco, CaliforniaSearch for more papers by this authorEtan Marks DO, Etan Marks DO UT Southwestern/Cockerell Dermatopathology, Dallas, TexasSearch for more papers by this authorLeah Persad DO, Leah Persad DO UT Southwestern/Cockerell Dermatopathology, Dallas, TexasSearch for more papers by this authorClay J. Cockerell MD, MBA, Clay J. Cockerell MD, MBA UT Southwestern/Cockerell Dermatopathology, Dallas, TexasSearch for more papers by this authorPhil Leboit MD, Phil Leboit MD Pathology Department, University of California San Francisco, San Francisco, CaliforniaSearch for more papers by this authorShane A. Meehan MD, Corresponding Author Shane A. Meehan MD shane.meehan@nyumc.org The Ronald O. Perelman Department of Dermatology, New York University School of Medicine, New York, New York Correspondence Shane A. Meehan, MD, The Ronald O. Perelman Department of Dermatology, New York University School of Medicine, New York, New York 240 E. 38th Street, 11th Floor, New York, NY 10016. Email: shane.meehan@nyumc.orgSearch for more papers by this author First published: 22 May 2019 https://doi.org/10.1111/cup.13513Citations: 1Read the full textAboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat No abstract is available for this article.Citing Literature Volume46, Issue10October 2019Pages 798-799 RelatedInformation

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.

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.

We present a compact dual-view endoscope objective lens with a field of view (FOV) of +/- 80 degrees 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 degrees, 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.

Satellite-borne laser altimeter measures the distance between a satellite and the earth through processing a laser echo signal collected by its receiving module. A laser echo simulation model for the ground-based distance parameter calibration of satellite-borne laser altimeter is proposed , in which the emission laser pulse and the returned laser pulse with an adjustable time-delay are generated. First, the time-delay value set in the laser echo simulation system was precisely measured by swapping two photodetectors and using a frequency counter, and the measurement error was 113 ps. The calibration of the elevation error is realized by comparing the time-delay set value and the time-delay value obtained in the receiving system. A laser echo simulation system is developed that offers distance simulation ability from 500 km to 550 km with a jitter of 34. 5 ps by setting the periodic time-delay from 3 335 640. 9 ns to 3 669 205. 0 ns. The time-delay accuracy of the laser echo simulation system for the satellite-borne laser altimeter is better than 118 ps and the system can provide a calibration capability better than 6 cm in the range of hundreds of kilometers.

Importance Extramammary Paget disease (EMPD), a rare intraepithelial adenocarcinoma, poses a therapeutic challenge with high postoperative recurrence rates and a limited number of effective local treatment options. Objective To describe the use and efficacy of a topical combination of fluorouracil and calcipotriene as a palliative therapy for refractory EMPD. Design, Setting, and Participants This retrospective case series of 3 women with recurrent, refractory EMPD was conducted at Beth Israel Deaconess Medical Center, Boston, Massachusetts and Washington University School of Medicine, St Louis, Missouri. All patients were treated with a 1:1 mixture of fluorouracil, 5%, cream and calcipotriene, 0.005%, cream or ointment. Main Outcomes and Measures Clinical and histopathological findings. Results All 3 women (1 in her 50s, 2 in their 70s) presented with recurrent EMPD (vulvar, perianal, and perioral) after surgery and/or irradiation, and their EMPD was refractory to treatment with imiquimod, 5%, cream. Owing to disease progression and/or intolerable adverse effects from imiquimod, the patients began treatment with a 1:1 mixture of fluorouracil, 5%, cream and calcipotriene, 0.005%, cream. This treatment, which was well tolerated, was followed by clinical improvement in symptoms and appearance of the lesions in all 3 cases and histopathological signs of decreased tumor burden in 2 cases. Patients applied the combination topical therapy to affected areas with differing frequencies, ranging from 1 to 2 days per month to 4 consecutive days every 2 weeks. Conclusions and Relevance Extramammary Paget disease frequently recurs even after aggressive surgical management and can be refractory to many topical and locoregional therapies. Palliative treatment with a combination of fluorouracil and calcipotriene may be a viable option for patients with recurrent, refractory EMPD.

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 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-theta 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. 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. (c) 2018 Optical Society of America

Partial null interferometry without using any null optics is proposed to measure a concave freeform Zernike mirror. Oblique incidence on the freeform mirror is used to compensate for astigmatism as the main component in its figure, and to constrain the divergence of the test beam as well. The phase demodulated from the partial nulled interferograms is divided into low-frequency phase and high-frequency phase by Zernike polynomial fitting. The low-frequency surface figure error of the freeform mirror represented by the coefficients of Zernike polynomials is reconstructed from the low-frequency phase, applying the reverse optimization reconstruction technology in the accurate model of the interferometric system. The high-frequency surface figure error of the freeform mirror is retrieved from the high-frequency phase adopting back propagating technology, according to the updated model in which the low-frequency surface figure error has been superimposed on the sag of the freeform mirror. Simulations verified that this method is capable of testing a wide variety of astigmatism-dominated freeform mirrors due to the high dynamic range. The experimental result using our proposed method for a concave freeform Zernike mirror is consistent with the null test result employing the computer-generated hologram.

The head-mounted display system is widely applied in the fields of modern education, medical treatment, and entertainment. The off-axis reflective head-mounted display optical system is a design form of head-mounted display system, and it can not only meet the requirements of miniaturization and compactness, but also realize broadband spectrum imaging without color aberration correction. However, the existing designs of off-axis reflective head-mounted display optical systems cannot compatibly meet the demands of large diameter of exit pupil and small F number together. To solve this problem, we design an off-axis head-mounted display optical system based on two reflective free-form surfaces to realize the requirements of large diameter of exit pupil and small F number. The double-curvature free-form surface and XY polynomial freeform surface are used in our designed head-mounted display optical system, its pupil diameter is 10 mm, F number is 3.0, field of view is 28 degrees and eye relief is larger than 15 mm. The final imaging performance of the system meets the requirements, and it is better than the current design results.

Modern advanced manufacturing and testing technologies allow the application of freeform optical elements. Compared with traditional spherical surfaces, an optical freeform surface has more degrees of freedom in optical design and provides substantially improved imaging performance. In freeform optics, the representation technique of a freeform surface has been a fundamental and key research topic in recent years. Moreover, it has a close relationship with other aspects of the design, manufacturing, testing, and application of optical freeform surfaces. Improvements in freeform surface representation techniques will make a significant contribution to the further development of freeform optics. We present a detailed review of the different types of optical freeform surface representation techniques and their applications and discuss their properties and differences. Additionally, we analyze the future trends of optical freeform surface representation techniques. (c) 2017 Society of Photo-Optical Instrumentation Engineers (SPIE)