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

Journal Article · Sun May 15 04:00:00 EDT 2016 · Review of Scientific Instruments

DOI:https://doi.org/10.1063/1.4950747· OSTI ID:22597925

Yashchuk, Valeriy V. ^[1]

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1. Advanced Light Source, Lawrence Berkeley National Laboratory, Berkeley, California 94720 (United States)

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.

• OSTI ID: 22597925
• Journal Information: Review of Scientific Instruments, Journal Name: Review of Scientific Instruments Journal Issue: 5 Vol. 87; ISSN 0034-6748; ISSN RSINAK
• Country of Publication: United States
• Language: English

Related Subjects

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND TECHNOLOGY
BEAMS
COMPUTERIZED SIMULATION
DIFFRACTION
DISTANCE
EXPECTATION VALUE
INCIDENCE ANGLE
MINIMIZATION
MIRRORS
OPTICAL SYSTEMS
OPTICS
POWER DISTRIBUTION
REFLECTIVITY
REGRESSION ANALYSIS
SHAPE
SURFACES
TUNING
WAVELENGTHS