High-harmonic diffractive lens color compensation.

Large diameter, high-harmonic diffractive lenses could find applications in future space telescopes. Residual chromatic aberrations from these lenses can cause significant blurring. Solutions to reduce chromatic dispersion and other aberrations to diffraction-limited performance are discussed. A design example based on a 240-mm-diameter, 1-m focal length multi-order diffractive engineered lens operating over the astronomical R-Band (589-727 nm) is presented. The design example uses a relay subsystem with four times smaller diameter than the primary. This color corrector includes both refractive and diffractive optical elements and reduces the longitudinal chromatic aberrations by more than a factor of 30 compared to the primary lens alone, while maintaining the effective focal length and numerical aperture of the system.

Precision glass molding of diffractive optical elements with high surface quality.

Diffractive optical surfaces have attractive properties for use in optical systems, like reducing weight and correcting for chromatic aberrations, but fabrication of high-quality glass diffractive optics is challenging, preventing it from being widely adopted in commercial applications. In this Letter, we report on a fabrication method to address molding challenges for high-surface-quality diffractive glass optics at molding temperatures up to 550°C, including selection of mold material, mold fabrication, precision glass molding, durability, and stability of the mold. To enable optimal mold machining and easy mold release, nickel phosphorous (NiP) is chosen as the plating material for its cutting performance and anti-adhesion properties, and copper-nickel C71500 (CuNi) is selected as the mold substrate because its coefficient of thermal expansion (CTE) is close to NiP. By the proposed method, diffractive glass optics with 2 nm Sa surface roughness is demonstrated.

Multiple-order diffractive engineered surface lenses.

A multiple-order diffractive engineered surface (MODE) lens is introduced, in which focal position change with wavelength exhibits both refractive and diffractive characteristics. Engineering calculations are provided that indicate Strehl ratio and encircled energy performance over a large range of focal length and aperture diameter design space. A prototype lens is designed and constructed for the astronomical R-band (589 nm to 727 nm) wavelength range. Test results show that measured full-width-at-half-maximum focal spot diameter is 2.1 times larger than the ideal Airy spot diameter, and focal position versus wavelength is nearly identical to the design. The 48 mm aperture diameter, f/3.12 prototype telescope exhibits angularly resolved features in natural scenes at 0.006°, with subtense of the Airy spot diameter at 0.002°. Applications include eventual use in large aperture, ultralightweight space telescopes.

Phase retrieval and adaptive optics correction for systems with diffractive surfaces.

Adaptive optics (AO) is a powerful technique for correcting extrinsic aberrations, such as those caused by atmospheric turbulence or biological sample thickness variations, by using measured phase information and a wavefront-correcting element. To extend AO techniques to systems with diffractive surfaces, considerations need to be made for additional components of the measured phase that are attributable to diffraction from the object and are not a part of the extrinsic aberration. For example, light reflected from a diffractive surface of an optical storage disk contains an additional phase due to the diffracted orders from the grating-like structure of the data tracks. In this work, a modified Gerchberg algorithm is presented as a viable method of phase retrieval to detect the total aberration, and correction for extrinsic aberrations is shown for light reflected from a grating. An experimental microscope system demonstrates successful AO correction, thus verifying simulation results.

Single-shot phase retrieval with complex diversity.

The concept of complex diversity is introduced that adequately accounts for special considerations in the design of the system and the reconstruction algorithm for single-shot phase retrieval techniques. Complex-number pupil filters containing both amplitude and phase values are extracted by numerical propagation from a computer-generated hologram design, which generates multiple images in a single acquisition. The reconstruction is performed by a Fourier iterative algorithm modified with an area restriction to avoid noise amplification. Numerical simulations show that the complex diversity technique estimates extrinsic Kolmogorov aberration better than conventional single-shot techniques for a distant point object. Experiments show that sensorless adaptive optics correction is achieved using the complex diversity technique.

Optimization of random phase diversity for adaptive optics using an LCoS spatial light modulator.

Phase retrieval is an attractive approach for sensor-less adaptive optics (AO) because of its relatively simple implementation. Recently, random phase diversity has shown fast convergence for phase retrieval algorithms. In this study, design optimization using random phase diversity is discussed with respect to a sensor-less AO system using a liquid-crystal-on-silicon (LCoS) spatial light modulator. The extrinsic phase disturbances studied are due to Kolmogorov turbulence. Simulation analysis shows that the size of super-pixel segments of the random phase patterns on the LCoS and the cropped image area of the phasorgrams are determined by Fried's parameter for high-Strehl-ratio and low-iteration-number reconstruction. AO experiments with an LCoS spatial light modulator confirm the simulation results.

Strehl ratio for optical systems with ultrafast illumination.

We study ultrafast laser pulse properties as they propagate through optical systems. A modified definition of Strehl ratio is used to quantify the chromatic and temporal behavior of ultrafast laser pulses at the optical focus. We propose this parameter as a figure of merit for the design and analysis of optical systems with ultrafast illumination. A simple method to obtain approximate numerical solutions is given with the help of ray tracing software. Effects of monochromatic aberrations and material dispersion up to the second order are discussed.

Fast fabrication of polymer out-of-plane optical coupler by gray-scale lithography.

We report a fabrication process of a polymer, and mirror-based out-of-plane optical coupler. In the process, a pre-formed mirror blank made of a buffer coat material is re-exposed by a laser direct writing tool with low numerical aperture of 0.1. The fabrication process is inherently fast because of the low numerical aperture (NA) process. The surface figure of the mirror is controlled under 0.04 waves in root-mean-square (RMS) at 1.55 µm wavelength, with mirror angle of 45 ± 1 degrees. Nominal insertion loss of 8.5dB of the mirror-based coupler was confirmed with polymer waveguides fabricated simultaneously.

Transfer function analysis in epi-illumination Fourier ptychography.

This Letter explores Fourier ptychography (FP) using epi-illumination. The approach effectively modifies the FP transfer function to be coherent-like out to the incoherent limit of twice the numerical aperture over the wavelength 2NA/λ. Images reconstructed using this approach are shown to have higher contrast at finer details compared with images using incoherent illumination, indicating that the FP transfer function is superior in high spatial frequency regions.

Analysis of grating doublets for achromatic beam-splitting.

Achromatic beam-splitting grating doublets are designed for both continuous phase and binary phase gratings. By analyzing the sensitivity to lateral shifts between the two grating layers, it is shown that continuous-profile grating doublets are extremely difficult to fabricate. Achromatic grating doublets that have profiles with a constant first spatial derivative are significantly more resistant to lateral shifts between grating layers, where one design case showed a 17 times improvement in performance. Therefore, binary phase, multi-level phase, and blazed grating doublets perform significantly better than continuous phase grating doublets in the presence of a lateral shift between two grating layers. By studying the sensitivity to fabrication errors in the height of both grating layers, one grating layer height can be adjusted to maintain excellent performance over a large wavelength range if the other grating layer is fabricated incorrectly. It is shown in one design case that the performance of an achromatic Dammann grating doublet can be improved by a factor of 215 if the heights of the grating layers are chosen to minimize the performance change in the presence of fabrication errors.

Sensitivity analysis and optimization method for the fabrication of one-dimensional beam-splitting phase gratings.

A method to design one-dimensional beam-spitting phase gratings with low sensitivity to fabrication errors is described. The method optimizes the phase function of a grating by minimizing the integrated variance of the energy of each output beam over a range of fabrication errors. Numerical results for three 1x9 beam splitting phase gratings are given. Two optimized gratings with low sensitivity to fabrication errors were compared with a grating designed for optimal efficiency. These three gratings were fabricated using gray-scale photolithography. The standard deviation of the 9 outgoing beam energies in the optimized gratings were 2.3 and 3.4 times lower than the optimal efficiency grating.

Hyper-numerical aperture (NA = 2.8) microscope using λ = 1.56 µm femtosecond source for multi-photon imaging.

A new microscope is discussed, where the scanning illumination has a numerical aperture of 2.8 with λ = 1.56 µm femtosecond fiber laser. Samples are placed or grown on a silicon substrate. Multi-photon emission is imaged in transmission on a cooled CCD. Two-photon and three-photon effects are observed from the silicon/water interface and gold nanoparticles. Images of cells, reference spheres and gold nanoparticles illustrate imaging properties of the microscope. Spectral characteristics of individual particles are achieved with a blazed transmission grating. Emission properties of differently sized gold nanoparticles are studied in detail, which indicate that their emission is a two-photon effect due continuum generation. Interestingly, spectral shape and emission power are similar for 20nm, 40nm and 60nm diameter gold nanoparticles for the cases studied.

Spot distribution measurement using a scanning nanoslit.

A scanning and rotating nanoslit is used to measure submicrometer features in focused spot distributions. Using a filtered backprojection technique, a highly accurate reconstruction is demonstrated. Experimental results are confirmed by simulating the scanning slit technique using a physical optics simulation program. Analysis of various error mechanisms is reported, and the reconstruction algorithm is determined to be very resilient. The slit is 125 nm wide and 50 µm long and is fabricated on a 120 nm thick layer of aluminum. The size of the image field is 15 µm, and simulations indicate that 200 nm Rayleigh resolution is possible with an infinitely narrow slit.

Microscope system for Blu-ray disc samples.

We introduce a microscope system using a solid immersion lens (SIL) to image Blu-ray disc samples without removing the protective cover layer. The aberration caused by the cover layer is minimized with a truncated SIL. A subsurface imaging simulation is achieved by using the rigorous coupled wave theory, partial coherence, vector diffraction, and the Babinet principle. Simulated results are compared with experimental images and atomic force microscopy measurements.

Effects of structured mid-spatial frequency surface errors on image performance.

Optical designers are encouraged to adopt aspheric and free-form surfaces into an increasing number of design spaces because of their improved performance. However, residual tooling marks from advanced aspheric fabrication techniques are difficult to remove. These marks, typically in the mid-spatial frequency (MSF) regime, give rise to structured image artifacts. Using a theory developed in previous publications, this paper applies the fundamentals of MSF modeling to demonstrate how MSF errors are evaluated and toleranced in an optical system. Examples of as-built components with MSF errors are analyzed using commercial optical design software.

Illumination artifacts in hyper-NA vector imaging.

Off-axis polarized monopole illumination is applied to a hyper-numerical-aperture (NA) (NA>1) microscopic system. Illumination artifacts due to vector effects are observed, which are asymmetric and depend on illumination conditions. A model based on rigorous coupled wave theory is used to simulate image profiles for dielectric, semiconductor, and metal gratings with different monopole locations and polarization states. A solid immersion lens microscope is used to image different types of samples including MoSi photomask, patterned silicon wafer, and chrome photomask. The experimental images are in good agreement with simulation results.

Theory of point-spread function artifacts due to structured mid-spatial frequency surface errors.

Optical design and tolerancing of aspheric or free-form surfaces require attention to surface form, structured surface errors, and nonstructured errors. We describe structured surface error profiles and effects on the image point-spread function using harmonic (Fourier) decomposition. Surface errors over the beam footprint map onto the pupil, where multiple structured surface frequencies mix to create sum and difference diffraction orders in the image plane at each field point. Difference frequencies widen the central lobe of the point-spread function and summation frequencies create ghost images.

Theory of modulation transfer function artifacts due to mid-spatial-frequency errors and its application to optical tolerancing.

Aspheric and free-form surfaces are powerful surface forms that allow designers to achieve better performance with fewer lenses and smaller packages. Unlike spheres, these surfaces are fabricated with processes that leave a signature, or "structure," that is primarily in the mid-spatial-frequency region. These structured surface errors create ripples in the modulation transfer function (MTF) profile. Using Fourier techniques with generalized functions, the drop in MTF is derived and shown to exhibit a nonlinear relationship with the peak-to-valley height of the structured surface error.

Characteristics of a scanning nano-slit image sensor for line-and-space patterns.

A single scanning nano-slit is used to study aerial image characteristics. Finite-difference time-domain simulations reveal that, in the far field of such a slit, the detected image contrast is very high over a large spatial frequency range regardless of the polarization direction. In the near field, the TM polarization shows a decrease in contrast at larger spatial frequencies. Experiments verify this characteristic using a 125 nm wide slit on an aluminum mask at a wavelength of 658 nm. Unlike the light transmission characteristics of a nano-slit, which are greatly influenced by slit width and metal mask thickness, it is shown that image contrast measurement is almost insensitive to small changes in these parameters. It is found that defects on the metal mask play an important role in accurate analysis of the system.

High-numerical-aperture image simulation using Babinet's principle.

Simulation techniques are developed for high-numerical-aperture (NA) polarized microscopy with Babinet's principle, including partial coherence and vector diffraction for non-periodic geometries. The model includes vector illumination and diffraction in high-NA (up to NA=3.5) object space that is imaged into low-NA image space and recorded on an image sensor. A mathematical model for the Babinet approach is developed and interpreted that includes partial coherence using expanded mutual intensity, where object reflective characteristics modify the coherence functions. Simulation results of the Babinet's principle approach are compared with those of rigorous coupled wave theory (RCWT) for periodic structures to investigate the accuracy of this approach and its limitations.