Null Lens Research Articles

Mapping distortion correction in off-axis aspheric mirror testing with a null compensator.

Mapping distortion can be introduced in null testing for off-axis aspheric surfaces, from which the testing results with coordinate deviation cannot be used to guide deterministic optical manufacturing. We propose a correction method for mapping distortion in this study based on the imaging distortion analysis of a null lens and iteration algorithm. We use imaging distortion data to fit the distortion polynomial function by the least-squares method, and we design an iteration algorithm to determine the rotation angle and the position of the null distortion point of the testing results. Finally, the mapping distortion can be accomplished without any markers on the mirror under test. The 280mm×180mm primary mirror and 234mm×176mm tertiary mirror of the hyperspectral camera were tested with a null compensator, and the distortion correction results were obtained using the proposed method. After magnetorheological finishing based on the correction results, the rms of the primary mirror and tertiary mirror reduced from 0.263λ to 0.013λ and 0.059λ to 0.018λ (λ=632.8nm), respectively.

Near-null interferometric test of aspheric cylinders utilizing a partial null lens

Aspheric cylinders are more advantageous than cylinder with spherical cross section in optical design and aberration correction of high-energy laser systems because additional shape parameters can be introduced. To overcome the limited test accuracy and the insufficient research on the testability of the flexible null test method for aspheric cylinders, a near-null interferometric test method for aspheric cylinders was developed utilizing a partial null lens. A coaxial configuration design was employed. Accordingly, only one translation motion was required for testing various aspheric cylinders in one shot. Using the proposed test configuration and the developed near-null data processing method, test accuracy about λ/20 (λ = 632.8 nm) root-mean-square are easier to guarantee compared with those of the existing stitching-required method with off-axis configuration. Further, the testability of the proposed method was analyzed following the development of the partial null theory. The analysis shows the testable surfaces are equidistant surfaces with nearly constant k·R products (k·R = 211.625 mm). The testability results can serve as a good reference for engineers who intend to use aspheric cylinders in high-energy laser systems and can further promote the development of high-energy laser systems. A near-null test system was established. Its simple configuration, moderate test accuracy, and flexible test capacity were successfully demonstrated based on aspheric cylinders measurements.

Near-null interferometry using an aspheric null lens generating a broad range of variable spherical aberration for flexible test of aspheres.

A null lens moving back and forth relative to a point source can generate variable spherical aberration for flexible test of aspheres. Different from the previous methods, variable spherical aberration null theory was developed by us to optimize the null lens. The optimized null was a plano-convex singlet containing a high order even asphere. Its attractive advantages are the simple structure and the broad range of testable surfaces. Most concave prolate conic and near conic surfaces with k∙R value varying between 0 and about 70000mm and with smaller relative aperture than that determined by each k∙R value can be tested. The testable asphericity range is between 0 and about 230λ. Relations among these testable surfaces were revealed as different groups of equidistant surfaces. To explicitly show the ability of the null, the measurable surfaces range map that contains all parameters defining a conic surface was offered. A practical near-null test system using this null was established. Alignment, near-null data processing, and error sources are analyzed in detail. To verify the broad testable surfaces range, three surfaces with widely varying amounts of asphericity were tested. Cross tests were provided to verify the test system accuracy.

Optical design of a null test of a synthetic reflective mirror based on the subaperture test method

Machining multiple mirror surfaces on one common substrate during the fabrication of off-axis three-mirror or four-mirror optical systems can take less time and drastically improve the alignment efficiency. However, the difficulty of the surface test remains the same. We theoretically propose a subaperture test method to carry out the null test of two mirrors on the synthetic reflective mirror. Specifically, we design a special zoom null lens and selectively use its subaperture wavefront aberrations of different configurations to nullify the surface normal wavefront aberrations of the according mirrors on the synthetic reflective mirror. The proposed method is verified by simulating the null test process of a synthetic reflective mirror integrating an off-axis high-order primary mirror (PM) and a coaxial high-order tertiary mirror (TM) of one off-axis three-mirror system, with the consideration of the fabrication and alignment errors. Simulation results show that, within a limited range of feasible tolerances, the residual wavefront aberration is 0.033λ root mean square (RMS) for the PM and 0.025λ RMS for the TM, at a wavelength of 1064 nm.

Verification and in situ calibration of large-aperture null correctors for convex aspheric mirrors

Interferometric test of large convex aspheres with high accuracy is still an urgent problem. Adopting a large-aperture null corrector is usually inevitable, and it is imperative to certify the large-aperture null optics in case incorrect final shape of the aspheric mirror is obtained. Moreover, it is necessary to calibrate and remove errors of the large-aperture null lens and trace errors to surfaces that are easy to obtain high accuracy. For these purpose, this paper presents an in situ calibrated null test method. The large-aperture null corrector for convex aspheric mirror is verified and calibrated by a wisely designed small aperture certifying null whose surfaces are either flat or spherical which are easy to be fabricated, measured and assembled. A redundant test is implemented by a Zygo VeriFire Asphere interferometer for cross test. Compared with existing methods of certificating null correctors which utilize an expensive CGH or a self-aligning aspherical mirror, the presented method finally traces errors of a large-aperture null corrector to small aperture flat and spherical surfaces thus costs are expected to be saved dramatically.

β1‐integrin controls cell fate specification in early lens development

Integrins are heterodimeric cell surface molecules that mediate cell-extracellular matrix (ECM) adhesion, ECM assembly, and regulation of both ECM and growth factor induced signaling. However, the developmental context of these diverse functions is not clear. Loss of β1-integrin from the lens vesicle (mouse E10.5) results in abnormal exit of anterior lens epithelial cells (LECs) from the cell cycle and their aberrant elongation toward the presumptive cornea by E12.5. These cells lose expression of LEC markers and initiate expression of the Maf (also known as c-Maf) and Prox1 transcription factors as well as other lens fiber cell markers. β1‐integrin null LECs also upregulate the ERK, AKT and Smad1/5/8 phosphorylation indicative of BMP and FGF signaling. By E14.5, β1-integrin null lenses have undergone a complete conversion of all lens epithelial cells into fiber cells. These data suggest that shortly after lens vesicle closure, β1-integrin blocks inappropriate differentiation of the lens epithelium into fibers, potentially by inhibiting BMP and/or FGF receptor activation. Thus, β1-integrin has an important role in fine-tuning the response of the early lens to the gradient of growth factors that regulate lens fiber cell differentiation.

Problems in the application of a null lens for precise measurements of aspheric mirrors.

Problems in the application of a null lens for surface shape measurements of aspherical mirrors are discussed using the example of manufacturing an aspherical concave mirror for the beyond extreme ultraviolet nanolithographer. A method for allowing measurement of the surface shape of a sample under study and the aberration of a null lens simultaneously, and for evaluating measurement accuracy, is described. Using this method, we made a mirror with an aspheric surface of the 6th order (i.e., the maximum deviation from the best-fit sphere is 6.6 μm) with the parameters of the deviations from the designed surface PV=5.3 nm and RMS=0.8 nm. An approximation of the surface shape was carried out using Zernike polynomials {Z(n)(m)(r,φ),m+n≤36}. The physical limitations of this technique are analyzed. It is shown that for aspheric measurements to an Angstrom accuracy, one needs to have a null lens with errors of less than 1 nm. For accurate measurements, it is necessary to establish compliance with the coordinates on the sample and on the interferogram.

Feedback Regulation of Intracellular Hydrostatic Pressure in Surface Cells of the Lens

In wild-type lenses from various species, an intracellular hydrostatic pressure gradient goes from ∼340 mmHg in central fiber cells to 0 mmHg in surface cells. This gradient drives a center-to-surface flow of intracellular fluid. In lenses in which gap-junction coupling is increased, the central pressure is lower, whereas if gap-junction coupling is reduced, the central pressure is higher but surface pressure is always zero. Recently, we found that surface cell pressure was elevated in PTEN null lenses. This suggested disruption of a feedback control system that normally maintained zero surface cell pressure. Our purpose in this study was to investigate and characterize this feedback control system. We measured intracellular hydrostatic pressures in mouse lenses using a microelectrode/manometer-based system. We found that all feedback went through transport by the Na/K ATPase, which adjusted surface cell osmolarity such that pressure was maintained at zero. We traced the regulation of Na/K ATPase activity back to either TRPV4, which sensed positive pressure and stimulated activity, or TRPV1, which sensed negative pressure and inhibited activity. The inhibitory effect of TRPV1 on Na/K pumps was shown to signal through activation of the PI3K/AKT axis. The stimulatory effect of TRPV4 was shown in previous studies to go through a different signal transduction path. Thus, there is a local two-legged feedback control system for pressure in lens surface cells. The surface pressure provides a pedestal on which the pressure gradient sits, so surface pressure determines the absolute value of pressure at each radial location. We speculate that the absolute value of intracellular pressure may set the radial gradient in the refractive index, which is essential for visual acuity.

大口径离轴非球面补偿检测的畸变校正

大口径离轴非球面补偿检测的畸变校正

Fabrication and calibration of an aspheric null lens in the testing of a large convex aspheric mirror

Fabrication and calibration of an aspheric null lens in the testing of a large convex aspheric mirror

倾斜计算全息板标定补偿器误差

倾斜计算全息板标定补偿器误差

Non-null annular subaperture stitching interferometry for steep aspheric measurement.

A non-null annular subaperture stitching interferometry (NASSI), combining the subaperture stitching ideal and non-null test method, is proposed for steep aspheric testing. Compared with standard annular subaperture stitching interferometry (ASSI), a partial null lens (PNL) is employed as an alternative to the transmission sphere, to generate different aspherical wavefronts as the references. The coverage subaperture number would be reduced greatly for the better performance of aspherical wavefronts in matching the local slope of aspheric surfaces. In this way, relatively large overlapping areas can be obtained for adjustment errors correction while the error accumulation would be decreased. With the reverse optimization reconstruction (ROR) method for retrace error correction, the figure error of each subaperture can be retrieved accurately. Therefore, the testing accuracy and efficiency are thus increased. The dynamic test range is extended as well. A numerical simulation exhibits the comparison of the performance of the NASSI and standard ASSI, which demonstrates the high accuracy of the NASSI in testing steep aspheric. Experimental results of NASSI are shown to be in good agreement with those of the Zygo interferometer.

The roles of αV integrins in lens EMT and posterior capsular opacification

Posterior capsular opacification (PCO) is the major complication arising after cataract treatment. PCO occurs when the lens epithelial cells remaining following surgery (LCs) undergo a wound healing response producing a mixture of α-smooth muscle actin (α-SMA)-expressing myofibroblasts and lens fibre cells, which impair vision. Prior investigations have proposed that integrins play a central role in PCO and we found that, in a mouse fibre cell removal model of cataract surgery, expression of αV integrin and its interacting β-subunits β1, β5, β6, β8 are up-regulated concomitant with α-SMA in LCs following surgery. To test the hypothesis that αV integrins are functionally important in PCO pathogenesis, we created mice lacking the αV integrin subunit in all lens cells. Adult lenses lacking αV integrins are transparent and show no apparent morphological abnormalities when compared with control lenses. However, following surgical fibre cell removal, the LCs in control eyes increased cell proliferation, and up-regulated the expression of α-SMA, β1-integrin, fibronectin, tenascin-C and transforming growth factor beta (TGF-β)–induced protein within 48 hrs, while LCs lacking αV integrins exhibited much less cell proliferation and little to no up-regulation of any of the fibrotic markers tested. This effect appears to result from the known roles of αV integrins in latent TGF-β activation as αV integrin null lenses do not exhibit detectable SMAD-3 phosphorylation after surgery, while this occurs robustly in control lenses, consistent with the known roles for TGF-β in fibrotic PCO. These data suggest that therapeutics antagonizing αV integrin function could be used to prevent fibrotic PCO following cataract surgery.

新型椭球形窗口零位检测技术研究

The elliptical windows testing technology has become the biggest block of development. In order to resolve the problem, the present testing technology for the asphere is expressed briefly. For the elliptical windows characterized by large tilt and large eccentricity deep asphere, based on the compensation theory, an improved Offner null testing compensator system for elliptical windows test is designed. The testing system includes compensator lens, field lens and a spherical reference mirror. The principle of Offner's refractive null lens testing system is that when parallel light from interferometer passes through the compensator lens and the field lens, correction wavefront is produced. After transmission through elliptical window and reflection of spherical reference mirror, light returns back according the original path and interferes with the reference light. The interference results display elliptical window shape deviation. The null lens testing system is implemented and the whole design results are demonstrated. For the tested elliptical window with fineness ratio of 1.0 and aperture of 110 mm, the root-mean-square (RMS) value of the final residual wavefront error is 0.0052. Design results provide a certain reference to pratical applications.

Etch depth mapping of phase binary computer-generated holograms by means of specular spectroscopic scatterometry

Detailed analysis of etch depth map for phase binary computer-generated holograms intended for testing aspheric optics is a very important task. In particular, diffractive Fizeau null lenses need to be carefully tested for uniformity of etch depth. We offer a simplified version of the specular spectroscopic scatterometry method. It is based on the spectral properties of binary phase multi-order gratings. An intensity of zero order is a periodical function of illumination light wave number. The grating grooves depth can be calculated as it is inversely proportional to the period. Measurement in reflection allows one to increase the phase depth of the grooves by a factor of 2 and measure more precisely shallow phase gratings. Measurement uncertainty is mainly defined by the following parameters: shifts of the spectrum maximums that occur due to the tilted grooves sidewalls, uncertainty of light incidence angle measurement, and spectrophotometer wavelength error. It is theoretically and experimentally shown that the method we describe can ensure 1% error. However, fiber spectrometers are more convenient for scanning measurements of large area computer-generated holograms. Our experimental system for characterization of binary computer-generated holograms was developed using a fiber spectrometer.

Bridging integrator protein 3 (Bin3) deletion causes cataract due to morphological abnormalities in lens cells

The lens is a complex epithelial tissue whose highly organized structure is required for its transparency. The BAR superfamily of peripheral membrane proteins control membrane curvature in many contexts and deletion of the BAR family member, Bin3, from mice results in cataracts (a clouding of the lens) associated with actin defects. However, the role that Bin3 plays in postnatal lens development and homeostasis is not known.Hematoxylin and Eosin staining of Bin3 null lenses revealed minor defects in fiber cell packing from birth to 3 weeks postnatal. The defects in fiber cell packing became progressively worse from 1 month until the fiber cells exhibited both vacuoles and disrupted fiber cell packing by 2 months. Scanning electron micrographs show that the elaborate membrane protrusions found on normal lens fiber cells becomes disorganized in Bin3 null lenses. The observed actin defects along with the morphological defect lead us to hypothesize that Bin3 is important for actin nucleation along lens fiber cell lateral membranes. Multiple proteins such as Cdc42, N‐WASP, and ARP2/3 control actin nucleation. In yeast Bin3 recruits Cdc42 to the cell division site and facilitates its activation, thus changing the cytoskeleton. It has not been shown whether this process is conserved in mammalian cells. Current studies suggest that Cdc42 plays a role in changing the cytoskeleton in Bin3 null lenses.Funded by NEI EY12221.Grant Funding Source: NEI EY 12221

Adjustable bipod flexures for mounting mirrors in a space telescope

A new mirror mounting technique applicable to the primary mirror in a space telescope is presented. This mounting technique replaces conventional bipod flexures with flexures having mechanical shims so that adjustments can be made to counter the effects of gravitational distortion of the mirror surface while being tested in the horizontal position. Astigmatic aberration due to the gravitational changes is effectively reduced by adjusting the shim thickness, and the relation between the astigmatism and the shim thickness is investigated. We tested the mirror interferometrically at the center of curvature using a null lens. Then we repeated the test after rotating the mirror about its optical axis by 180° in the horizontal setup, and searched for the minimum system error. With the proposed flexure mount, the gravitational stress at the adhesive coupling between the mirror and the mount is reduced by half that of a conventional bipod flexure for better mechanical safety under launch loads. Analytical results using finite element methods are compared with experimental results from the optical interferometer. Vibration tests verified the mechanical safety and optical stability, and qualified their use in space applications.

Technology on Fabrication of Precise SiC Aspherical Mirror

This paper represents a technique to produce the large size optical aspherical mirror by using reaction-bonded silicon carbide to meet the material requirements of the space used mirrors, based on the characters comparison of all types mirror material. Techniques are described in this paper, including the bonding procedure of silicon carbide to form a mirror shape, the CCOM technology for aspheric grinding, polishing on a home-developed tool –FSGJ-2, and the aspheric profilometry. A specialized Offner Null lens is also developed to measure the aspherical mirror with laser interferometer. With the technology depicted in the paper, a 502mm x 298 mm off-axis SiC aspherical mirror is successfully made with a surface accuracy better than 1/50λrms, the final result meets the design requirement.

Subaperture stitching interferometry of high-departure aspheres by incorporating a variable optical null

Originally, subaperture stitching interferometry enabled full-aperture measurement of large-aperture spheres and flats using 4″ or 6″ interferometers and transmission elements. Later, mild aspheric surfaces could be measured using the same fundamental principles. In both cases, stitching algorithms automatically compensate for systematic reference wavefront and distortion errors. Aspheres with up to 1000 waves of departure from best-fit sphere can be measured without dedicated null lenses using a variable optical null (VON™) device which generates an optical wavefront that closely matches the surface of the asphere within a local subaperture. This paper presents the principles of subaperture stitching interferometry incorporating VON technology.

离轴非球面反射镜补偿检验的计算机辅助装调技术研究

Based on the principle of null lens,a new method of error-separation was proposed in null testing.A mathematic model was developed to separate misalignment-induced aberration from the test result.The method was used in the simulations of an off-axis aspheric mirror.The wavefront aberration induced by misalignment is 0.0026λRMS(λ=632.8 nm) after the alignment,compared with 0.2332λRMS before the alignment,which reflects that this method has high accuracy and can improve the efficiency of the null test.