Matthew B. Dubin

Implementation of sine condition test to measure optical system misalignments

Rather than measuring aberrations across the field to quantify the alignment of an optical system, we show how a single, on-axis measurement of the pupil mapping can be used to measure the off-axis performance of the system and determine the state of alignment. In this paper we show how the Abbe sine condition can be used to relate the mapping between the entrance and exit pupils to image aberrations that have linear field dependence. This mapping error then can be used to measure the linear astigmatism caused by the misalignment. Additionally, we present experimental results from the sine condition test on a simple system.

Design and optimization of the sine condition test for measuring misaligned optical systems

By taking a new look at an old concept, we have shown in our previous work how the Abbe sine condition can be used to measure linearly field-dependent aberrations in order to verify the alignment of optical systems. In this paper, we expand on this method and discuss the design choices involved in implementing the sine condition test (SCTest). Specifically, we discuss the two illumination options for the test: point source with a grating or flat-panel display, and we discuss the tradeoffs of the two approaches. Additionally, experimental results are shown using a flat-panel display to measure linearly field-dependent aberrations. Last, we elaborate on how to implement the SCTest on more complex optical systems, such as a three-mirror anastigmat and a double Gauss imaging lens system.

Use of the surface PSD and incident angle adjustments to investigate near specular scatter from smooth surfaces

The Rayleigh Rice vector perturbation theory has been successfully used for several decades to relate the surface power spectrum of optically smooth reflectors to the angular resolved scatter resulting from light sources of known wavelength, incident angle and polarization. While measuring low frequency roughness is relatively easy, the corresponding near specular scatter can be difficult to measure. This paper discusses using high incident angle near specular measurements along with profile generated surface power spectrums as a means of checking a near specular scatter requirement. The specification in question, a BRDF of 1.0 sr-1 at 2 mrad from the specular direction and at a wavelength of 1μm, is very difficult to verify by conventional scatter measurements. In fact, it is impractical to directly measure surface scatter from uncoated Zerodur because of its high bulk scatter. This paper presents profilometer and scatterometer data obtained from coated and uncoated flats at several wavelengths and outlines the analysis technique used to check this tight specification.

Simultaneous multi-segmented mirror orientation test system using a digital aperture based on sheared Fourier analysis

This paper presents a simultaneous multi-segmented mirror orientation test system (SMOTS) using localized sheared images. A CMOS camera captures images of reflected 2D sinusoidal patterns from the test mirrors as their orientation changes. Surface orientation is measured to within 0.8 µrad (0.16 arcseconds) for a flat mirror. In addition, we measure the variation of seven mirror segments simultaneously. Furthermore, SMOTS is applied to measure the orientation of two concave mirrors with an accuracy of 2.7 µrad (0.56 arcseconds). The measurement time for seven segments is 0.07 s. This technique can monitor the mirror segment orientation in an open/closed-loop for various optical setups.

Alignment of a three-mirror anastigmat using the sine condition test

Continuing to develop the sine condition test (SCTest), we show how violations of the generalized sine condition can be used to align a three-mirror anastigmat (TMA). This paper shows how the linear aberrations measured using the sine condition, along with aberrations that have constant field dependence, can be used to align a system. We discuss the design of the test hardware needed to align a TMA and the procedure for alignment. Using simulation, we then investigate the behavior of the alignment SCTest for various levels of mirror misalignment, mirror fabrication errors, and misalignment of the test equipment. All of these tests show that the alignment SCTest can successfully align an optical system.

Design and analysis of an alignment procedure using computer-generated holograms

A procedure that uses computer-generated holograms (CGHs) to align an optical system’s meters in length with low uncertainty and real-time feedback is presented. The CGHs create simultaneous three-dimensional optical references, which are decoupled from the surfaces of the optics allowing efficient and accurate alignment even for systems that are not well corrected. The CGHs are Fresnel zone plates, where the zero-order reflection sets tilt and the first-diffracted order sets centration. The flexibility of the CGH design can be used to accommodate a wide variety of optical systems and to maximize the sensitivity to misalignments. An error analysis is performed to identify the main sources of uncertainty in the alignment of the CGHs and to calculate the magnitudes in terms of general parameters, so that the total uncertainty for any specific system may be estimated. A system consisting of two CGHs spaced 1 m apart is aligned multiple times and re-measured with an independent test to quantify the alignment uncertainty of the procedure. The calculated and measured alignment uncertainties are consistent with less than 3 μrad of tilt uncertainty and 1.5 μm of centration uncertainty (1σ ).

Application of a synthetic extended source for interferometry

This paper presents the design of a synthetic extended source (SES) that reduces coherent noise in interferometric measurements. The SES uses a fully coherent source for data acquisition to preserve high-contrast interferograms. Multiple measurements are made while the point source is translated according to a prescribed trajectory. The average of the measurements has the effect of using a source with a distribution defined by the trajectory. Thus, the optical system uses a coherent point source, but the data combination synthesizes the behavior of an extended source. A parametric model to quantify measurement noise due to diffraction from small particles is developed and used to evaluate SES designs. Experimental results are shown that validate the modeling. An example of a practical working SES implemented in a custom SPSI interferometer is provided.

Use of a flat panel display for measurement of sine condition violations

Previous works have shown the viability of using the Sine Condition Test (SCTest) to verify the alignment of optical systems. The SCTest uses the Abbe sine condition to measure the mapping between the entrance and exit pupils of an optical system. From this pupil mapping, the linearly-field dependent aberrations can be measured and used to verify the alignment. Specifically, the linear astigmatism is used as a metric to determine how well the optical system is aligned. An advantage to using the sine condition to measure the off-axis performance is that the measurement equipment can be placed on-axis. By doing this, the uncertainty of the measurement is reduced, making this test especially useful for verifying systems with large inherent aberrations. In this paper, we expand the design space of the SCTest by exploring the two different source options: a point source with a grating or a flat-panel display. Additionally, we show experimental results of implementing the SCTest using a flat-panel display. Last, we explain how the SCTest can be implemented on more complex systems, such as a three-mirror anastigmat (TMA) and a double Gauss. By exploring the design space, we provide more design options for selecting the SCTest source, increasing the flexibility and utility of the SCTest.

Characterization of alignment using measurements of the sine condition

An experimental test for violations of the sine condition is presented. This test is particularly useful for identifying the state of alignment of an imaging system because it provides a direct measurement of the linear astigmatism (astigmatism that varies linearly with field) in a system using only on axis measurements. The concept of the test is explained from the perspective of both geometrical optics, using the sine condition, and wave optics. In addition, the results of an experimental proof of concept are presented. This experiment shows good agreement between the measured and predicted results.

Measurement results for time-delayed source interferometers for windows, hemispherical domes, and tangent ogives

A time-delayed source interferometer manipulates the output of a short-coherence length source so that light reflected from the two surfaces of a nominally constant-thickness optical component interfere. The interference pattern is a measure of optical thickness variation and can be phase-shifted. The approach is well suited to optical components that are nominally constant thickness over some portion of the surface. Interferometers suited to the measurement of windows, hemispherical domes and tangent ogives have been built. Data acquisition, calibration tooling and processing methods are described for the stitching of phase data.