A phase-recovery method based on iterative least-square fitting is proposed to overcome off-axis phase-shifting errors of high numerical-aperture (NA) surfaces in tilt phase-shift interferometry. Vibration of test optics having optical powers makes nonuniform off-axis phase-shift errors over the aperture, which is severe when testing optics with high NA. The proposed method calculates the test wavefront, off-axis phase shift, and tilt phase shifts in x- and y-directions within four separate least-square fitting steps iteratively. Parabolic and linear regressions are used for extracting off-axis and tilt phase-shift errors, respectively. The proposed method is verified with simulations and experiments with a Fizeau interferometer having F/0.75 transmission sphere. This method can be used with a temporal phase-shifting interferometers for testing high-NA optics in the presence of vibration.
We present the development of a 1-m lightweight mirror system for a spaceborne electro-optical camera. The mirror design was optimized to satisfy the performance requirements under launch loads and space environment. The mirror made of Zerodur® has pockets at the back surface and three square bosses at the rim. Metallic bipod flexures support the mirror at the bosses and adjust the mirror’s surface distortion due to gravity. We also show an analytical formulation of the bipod flexure, where compliance and stiffness matrices of the bipod flexure are derived to estimate theoretical performance and to make initial design guidelines. Optomechanical performances such as surface distortions due to gravity is explained. Environmental verification of the mirror is achieved by vibration tests.
We present our design method for a 1 m lightweight mirror in a space optical system. The mirror made of Zerodur® has pockets at the back surface and three square bosses at the rim. Metallic bipod flexures support the mirror at the bosses and adjust the mirror’s surface distortion due to gravity. Their dimensional parameters cannot be optimized independently from each other in a conventional design process, where the mirror’s optical performance is greatly influenced by the flexure configuration. With our method, the design problem is separated into two independent problems; mirror design and flexure design. Resources required to achieve the design goals are reduced by almost one order of magnitude in time. We implemented a multi-objective genetic algorithm to optimize the mirror design and satisfied the design goals. We also present a new adjustable bipod flexure as an optical compensator for the gravity-induced aberration, instead of using a monolithic bipod flexure.
For the purpose of fabricating off-axis aspheric optics, we propose a 8-axis-polishing machine combined with a testing
tower whose height is about 9 m. The proposed polishing machine was designed and analysed by using a well-known
finite element method. The eight axes of the machine have a synchronized motion generated by a computer, and each
axis was calibrated by a heterodyne laser interferometer or an optical encoder. The maximum capability of the proposed
polishing machine is up to 2 m in diameter, and the maximum radius of curvature of the product (optics) is slightly over
7 m. After calibration, the maximum positioning error of the machine was less than 2 μm within a whole 2 m × 2 m area.
A typical fabrication result of a φ1.5 m concave mirror was also described in this manuscript.
We present our design procedure for a 1-m lightweight mirror in a space optical system. The glass mirror has three monolithic bosses at the rim and is assembled with metallic bipod flexures. Their dimensional parameters cannot be optimized independently with each other in a classical design process, where optical performance is greatly affected by the flexure mount configuration. With our method, the design problem is separated into two independent problems; mirror design and flexure design. Resources required to achieve design goals are reduced by almost one order of magnitude in time. Also the mirror and flexure mount designs can be parallel-processed without interfering each other. In this paper, we present the mirror design process and its results optimized with multi-objective genetic algorithm (GA).
We explain a new lens mounting scheme using cascaded ring flexures for minimizing thermal stresses. Two
circular rings are concentric at the adhesive insertion hole and made monolithically on a lens cell. Six degree-of-freedom
motions can be accommodated by controlling dimensional parameters. Thermo-elastic deformations are
evaluated by interferometric measurements and are verified with finite element analyses. Athermal performances
from a simple elastomeric mount and a ring-flexured mount are also compared. This lens mounting scheme was
successfully applied to our space-borne optical system and will be a promising candidate for environmentally
challenged optical systems such as military applications.
We propose a new point diffraction interferometer using a polarizer with a pinholed for qualitative optical
analysis. Diffraction from a polarizer with a pinholed makes reference and measurement waves. Interference
fringe between diffracted-undiffracted measurement wave and undiffracted-diffracted reference wave is stabilized
by common-path configuration. We examined the pinhole size and divergence angle of the diffracted wave for
test optics with various numerical aperture. Optical parts comprising the interferometer can be assembled into a
small monolithic component and embedded into an imaging target for easy alignment. Optical systems evaluating
imaging performances such as modulation transfer function would benefit in aligning target objects.
We present a new type of point-diffraction interferometer specially designed for industrial use with high immunity to external vibration encountered in the course of measurement process. The proposed interferometer uses thermally-expanded fibers instead of conventional pinholes as the point-diffraction source to obtain a high quality reference wave with an additional advantage of relatively easy alignment of optical components. Vibration desensitization is realized through a common-path configuration that allows the influence of vibration to affect both the reference and measurement waves identically so that it is subsequently cancelled out during the interference of the two waves. A spatial phase shifter is added to capture four phase-shifted interferograms simultaneously without time delay using a single camera to avoid vibration effects. Experimental results demonstrate that the proposed interferometer is capable of providing stable measurements with a level of fringe stabilization of less than 1 nanometer in a typical workshop environment equipped with no excessive ground isolation for anti-vibration.
We present a new type of point diffraction interferometer that employs single-mode optical fibers instead of traditional pinholes. Two optical fibers with different exit endfaces are used; one is normally cut and the other obliquely cleaved. The normally cut fiber is used to generate a near-perfect spherical reference wave. The test wave is produced from the oblique fiber that performs two functions: generating a spherical wave to illuminate the test optics, and reflecting the test wave for common-path combination with the reference wave. The interferometer proposed in this investigation is found suitable for testing large size mirrors with a relatively simple overall hardware configuration.
We present a new type of point-diffraction interferometer specially designed for industrial use to obtain high immunity to external vibration encountered in the course of measurement process. The proposed interferometer uses thermally- expanded fibers instead of conventional pinholes as the point-diffraction source to obtain a high quality reference wave with an additional advantage of relatively easy alignment of interferometric optical setup. Vibration desensitization is realized through a common-path configuration that allows the influence of vibration to identically affect both the reference wave and the measurement wave and be subsequently cancelled out during the interference of the two waves. A new spatial phase shifter is also added to capture four phase-shifted interferograms simultaneously without time delay using a single camera to avoid vibration effect. Experimental results for a spherical concave mirror prove that the proposed interferometer is capable of providing stable measurements with a level of fringe stabilization of less than 1 nanometer in a typical workshop environment equipped with no excessive ground isolation for anti-vibration. Also, we verify that the proposed interferometer using a short coherence source is applicable to the surface metrology for defect inspection of transparent substrates such as liquid crystal display panels.
When optical fibers are connected with other optical or opto-mechanical components, free space propagation phenomena of the light emitted from cleaved end facets of fiber need to be precisely known to maximize coupling efficiency. Besides, optical fibers are widely used in interferometers design as point-diffraction sources to replace conventional pinholes, in which case the far-field wave front of the light emitted from fibers is of major concern. End facets may be cleaved normal to the optical axis of fibers or with oblique angles to suit specific purposes such as anti-reflection or propagation direction alteration. In this investigation, diffraction from oblique end facets of single-mode fibers is studied with emphasis on Fresnel propagation in nonparaxial zones based on the Rayleigh-Sommerfeld scalar diffraction theory. The result is a closed-form explicit solution expressed in terms of spherical coordinates, which enables to determine the propagation field generated over an entire hemispherical observation surface. In comparison to exiting solutions of numerical or infinite series forms, the explicit solution obtained in this investigation saves a considerable amount of computation time and provides better estimation accuracy. Finally, as an example, the wave front sphericity emitted from an oblique single-mode fiber used in a new design of the Fizeau interferometer is determined and discussed in detail.
We describe an oblique point-diffraction source, which is made from a single-mode optical fiber whose end is specially cut with an oblique face angle of 28.8° to the optical axis of the fiber. Analytical and empirical investigations reveal that, like ordinary fibers cut with zero face angle, the oblique fiber generates a high-quality spherical wave into free space by means of point diffraction at its end, but the diffracted wave has a propagation angle of 45° to the surface normal. This inclined nature of point diffraction is useful in many optical designs because it allows the returning wave of the original diffracted wave to be reflect at a right angle at the end face of the oblique fiber without additional optics. An exemplary use of the oblique fiber is demonstrated in an enhanced optical design of Fizeau interferometer, in which the troublesome combination of a pinhole and a beam splitter is effectively replaced only with a single oblique fiber. Another example is shown in a phase-shifting diffraction interferometer that has been specially designed for testing concave mirrors of low f-numbers. The use of oblique fibers enables to use the entire full numerical aperture of the diffracted wave from a single-mode fiber for optical testing without any overlap between the reference and the test waves.
Light emanating from the polished end of a single-mode fiber forms into a near-perfect spherical wave within a finite solid angle, which can readily be explained by diffraction theory. Utilizing the useful phenomenon, we in this paper present a fiber optic diffraction interferometer that has specially been devised for testing spherical mirrors. The interferometer adopts three optical fibers; one is for generating spherical reference wave, another is for illuminating the mirror under test and the other is for calibrating the interferometer. A special assembly of sliding prism driven by a PZT actuator provides necessary phase shifts with a high immunity to environmental disturbances. In conclusion, the proposed fiber optic diffraction interferometer enables us to achieve a measurement accuracy of an order of magnitude better than conventional testing schemes using the Fizeau interferometers of which measurement accuracy is ultimately limited by the reference surface to (lambda) /50, where λ is the wavelength of the source.