Optimized mirror shape tuning using beam weightings based on distance, angle of incidence, reflectivity, and power

Journal Article · Tue May 24 00:00:00 EDT 2016 · Review of Scientific Instruments

DOI:https://doi.org/10.1063/1.4950747· OSTI ID:1530233

Goldberg, Kenneth A. ^[1]; Yashchuk, Valeriy V. ^[2]

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1. Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
2. Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States). Advanced Light Source (ALS)

For glancing-incidence optical systems, such as short-wavelength optics used for nano-focusing, incorporating physical factors in the calculations used for shape optimization can improve performance. Wavefront metrology, including the measurement of a mirror's shape or slope, is routinely used as input for mirror figure optimization on mirrors that can be bent, actuated, positioned, or aligned. Modeling shows that when the incident power distribution, distance from focus, angle of incidence, and the spatially varying reflectivity are included in the optimization, higher Strehl ratios can be achieved. Following the works of Maréchal and Mahajan, optimization of the Strehl ratio (for peak intensity with a coherently illuminated system) occurs when the expectation value of the phase error's variance is minimized. We describe an optimization procedure based on regression analysis that incorporates these physical parameters. This approach is suitable for coherently illuminated systems of nearly diffraction-limited quality. Mathematically, this work is an enhancement of the methods commonly applied for ex situ alignment based on uniform weighting of all points on the surface (or a sub-region of the surface). It follows a similar approach to the optimization of apodized and non-uniformly illuminated optical systems. Significantly, it reaches a different conclusion than a more recent approach based on minimization of focal plane ray errors.

• Research Organization: Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)
• Sponsoring Organization: USDOE Office of Science (SC), Basic Energy Sciences (BES); USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)
• Grant/Contract Number: AC02-05CH11231
• OSTI ID: 1530233
• Alternate ID(s): OSTI ID: 1420625; OSTI ID: 22597925
• Journal Information: Review of Scientific Instruments, Journal Name: Review of Scientific Instruments Journal Issue: 5 Vol. 87; ISSN 0034-6748
• Publisher: American Institute of Physics (AIP)
• Country of Publication: United States
• Language: English

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