We devise analytical equations to design a radially symmetric optical system with three stigmatic pairs in the meridional plane. The optical system is composed by an arbitrary number of refractive surfaces. We test the model with ray-tracing techniques and the performance results as expected. The model presented here can be easily generalized for an arbitrary number of stigmatic pairs.

Anamorphic zoom lenses, used extensively in the motion picture industry, pose a significant design challenge, combining the difficulties of designing a high-performance zoom lens with those of designing an anamorphic lens. As a result, considerable emphasis must be placed on the first-order configuration of the starting point design before interfacing with optical design software. A Monte Carlo search method is introduced for generating first-order designs of anamorphic zoom lenses based on two different configurations. The obtained designs possess valid zoom motions and ray trace successfully while satisfying a set of system specifications. This search method offers a time effective and illustrative way of exploring the global solution space of first-order designs for use as starting points on the way to a thick lens, color-corrected final design. The results of such a Monte Carlo search are presented for two types of anamorphic zoom configurations, and a design example is demonstrated.

Optimal optical transfer function (OTF) is proposed for RGB inverse imaging with extended depth of field (DoF) and diminished color aberrations. This optimal OTF is derived as the Wiener filter of broadband defocused OTFs. The performance of this new inverse imaging is demonstrated for optical setups with lens and lensless with a multilevel phase mask instead of the lens. The later lensless system designed for the wavelength range (400 to 700) nm and DoF range (0.5 to 1000) m demonstrates the best performance.

The focusing of wide stripe laser diode astigmatic beams to be as small as possible spots for highest power densities is analyzed. The “best” and “worst” alignment situations are identified for the first time. The significant differences among the focused spot sizes obtained in the best and worst alignments are shown by software raytracing examples. It is found that the conventional understanding that expanding the beam many times in the slow axis direction with the worst alignment can decrease the smallest focused spot is not correct. It is also found that by properly aligning the lenses, the astigmatism in the focused beam can be eliminated.

We examine the characteristics of linear astigmatism in a nonaxially symmetric optical system. The conventional view of interpreting linear astigmatism aberration using P and N focal surfaces is revisited. A perspective to explain and visualize the behavior of linear astigmatism is provided using the concept of field curves. Methods of controlling linear astigmatism are discussed, including a ray-tracing method using pupil imaging. Confocal mirror designs free from linear astigmatism are also discussed.

Digital holographic microscopy can quantitatively image the biological samples label-free and noninvasively. It is key to extract the +1-term spectrum from the hologram spectrum, which is crucial to the quality of the reconstructed image. Therefore, an adaptive spatial filtering method based on fuzzy C-means and phase spectrum of a hologram is proposed to extract the +1-term spectrum without any prior knowledge. The maximum phase value point of phase spectrum is found, which must be located in the +1-term spectrum. Then, this point is first introduced to locate the +1-term spectrum region. Two classifications and three regions (+1-term, −1-term, and zero-order term spectra regions) are obtained by fuzzy C-means in the amplitude spectrum. Subsequently, the minimum distance between the centroids of the three regions and the maximum phase point is used to judge the +1-term spectrum region. Finally, a filtering window is obtained by the edge of the +1-term spectrum region and the +1-term spectrum is adaptively extracted. Compared to other spatial filtering methods, the proposed method avoids dependence on a prior custom mask and suppresses the higher frequency noise. Most importantly, the experimental results on a number of human cells and a phase step demonstrate the feasibility and efficiency of the proposed method.

We present two techniques to improve as-built miniature lenses that are defined with high-order aspheric surfaces without losing optical quality and without significantly modifying the layout of the lens. We note that miniature lenses are often defined with more aspheric coefficients than needed. This redundancy can lead to poor as-built lenses. The first technique consists of gradually reducing the number of high-order aspheric coefficients while reoptimizing the lens and maintaining the performance. The second technique consists of desensitizing the lens through a multi-configuration process where different configurations are defined and optimized at the same time. These are the nominal configuration and several perturbed configurations that include lens decenter and tilt. Both techniques are shown to work for improving as-built lenses as we show in two examples from the lens literature.

We present a new optical design of an off-axis three-mirror system (OTS) that is corrected for spherical, coma, astigmatism, and field curvature aberrations. Our design methodology begins using paraxial theory and continues with the third-order approach for a coaxial three-mirror system (CTS) with a wide field of view and high resolution. We propose to use only two optical elements because the primary and tertiary mirrors will be integrated in a single optical element, the secondary mirror will be the other optical element. For our final design, we will use only off-axis surfaces. Thus it will be possible to obtain a compact, light, easy-to-align optical system with high stability. However, when the CTS is transformed into an OTS, new aberrations are generated. The last step in our methodology is to use freeform surfaces to compensate for new aberrations. With this methodology, a limited diffraction system is obtained.

To measure large and heavy micro-structured workpieces in situ and improve the measurement accuracy, which strongly depends on the environment during the measurement of micro-structured surfaces, a workpiece rotating technique is proposed. This method utilizes the precise rotation of machine tools to drive the workpiece and records a set of elemental image arrays for the pickup stage to overcome the upper-resolution limit imposed by the Nyquist sampling theorem, which allows the increase in the two-dimensional spatial resolution of the computed depth images in integral imaging. By extracting the depth position, we can obtain accurate depth information and measurement results for micro-structured surfaces. We carried out simulations and experiments to demonstrate the proposed method, and the results show the feasibility of our method.