Condition Number as a Metric for the Effectiveness of Polarimetric Algorithms

Twietmeyer, Karen; Chipman, Russell A.

doi:10.1364/fio.2005.fmb5

Cited by 7 publications

(5 citation statements)

References 4 publications

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“…Many authors have shown more efficient calibration and modulation schemes based on retarders that are either elliptical or values that optimize the condition number of the demodulation matrix given an observing set. 15,47,48,60,68,[71][72][73][74][75][76][77] We can easily implement similar calibration schemes with our retarders when they do not happen to be the traditional quarter-wave linear retarder. As an example of the utility for this MgF 2 retarder for on-axis calibration with strong thermal behavior benefits, we show the linear retardance magnitude away from half-wave in Figure 35.…”

Section: Appendix B Spatial and Spectral Retardance Of Dkist Retardersmentioning

confidence: 99%

Polarization modeling and predictions for Daniel K. Inouye Solar Telescope part 4: calibration accuracy over field of view, retardance spatial uniformity, and achromat design sensitivity

Harrington

Sueoka

2018

J. Astron. Telesc. Instrum. Syst.

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Modern observatories and instruments require optics fabricated at larger sizes with more stringent performance requirements. The Daniel K. Inouye Solar Telescope (DKIST) will be the world's largest solar telescope at 4.0 m aperture delivering a 300 Watt beam and a 5 arc-minute field. Spatial variation of retardance is a limitation to calibration of the full field. Three polarimeters operate seven cameras simultaneously in narrow bandpasses from 380 nm to 1800 nm. The DKIST polarization calibration optics must be 120 mm in diameter at Gregorian focus to pass the beam and operate under high heat load, UV flux and environmental variability. Similar constraints apply to the three retarders for modulation within the instrument suite with large beams near focal planes at F/ 18 to F/ 62. We assess how design factors can produce more spatial and spectral errors simulating elliptical retardance caused by polishing errors. We measure over 5 • net circular retardance and spectral oscillations over ±2 • for optics specified as strictly linear retarders. Spatial variations on scales larger than 10 mm contain 90% of the variation. Different designs can be a factor of 2 more sensitive to polishing errors with dissimilar spatial distributions even when using identical retardance bias values and materials. The calibration for the on axis beam is not impacted once circular retardance is included. Calibration of the full field is limited by spatial retardance variation unless techniques account for this variation. We show calibration retarder variation at amplitudes of 1 • retardance for field angles greater than roughly one arc minute for both quartz and MgF 2 retarders at visible wavelengths with significant variation between the three DKIST calibration retarders. We present polishing error maps to inform new calibration techniques attempting to deliver absolute accuracy of system calibration below effective cross-talk levels of 1 • retardance.

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Section: Appendix B Spatial and Spectral Retardance Of Dkist Retardersmentioning

confidence: 99%

Polarization modeling and predictions for Daniel K. Inouye Solar Telescope part 4: calibration accuracy over field of view, retardance spatial uniformity, and achromat design sensitivity

Harrington

Sueoka

2018

J. Astron. Telesc. Instrum. Syst.

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“…Of course, calibration does not require only linear retardance and does not require particularly chromatic behavior. 15,[63][64][65][66][67][68][69][70][71][72][73] Elliptical, chromatic retarders are suitable, but the DKIST project decided to follow this common quarter-wave linear strategy at the time procurement decisions were made.…”

Section: Dkist Calibration Retardermentioning

confidence: 99%

Polarization modeling and predictions for DKIST part 2: application of the Berreman calculus to spectral polarization fringes of beamsplitters and crystal retarders

Harrington

Snik

Keller

et al. 2017

J. Astron. Telesc. Instrum. Syst

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“…The wavefront reconstruction accuracy evaluation method was described in detail in Section 2.3. Stability means that the anti-noise interference ability of the wavefront reconstruction process can be evaluated by the condition number of the reconstruction matrix [30,31]. The condition number is defined as: (11) where σ max and σ min represent the maximum and the minimum singular values of the reconstruction matrix Z, respectively.…”

Section: Maximum Recognizable Mode Order Of the Systemmentioning

confidence: 99%

Simulation Analysis of an Atmospheric Turbulence Wavefront Measurement System

Wang,

Qin,

et al. 2024

Photonics

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In this paper, a turbulent wavefront measurement model based on the Hartmann system structure is proposed. The maximum recognizable mode number of different lens units is discussed, and the influence of different lens array arrangements on the accuracy of turbulent wavefront reconstruction is analyzed. The results indicate that the increase in the aberration order of the turbulent wavefront has a certain influence on the reconstruction ability of the system. Different lens arrangements and number of lens units will lead to the effective reconstruction of different final mode orders. When using a 5 × 5 lens array arrangement and a hexagonal arrangement of 19 lenses, the maximum order of turbulent wavefront aberrations allowing for effective reconstruction was 25. When the sparse arrangement of 25 lenses or the sparse arrangement of 31 lenses was used, the maximum order allowing for effective reconstruction was 36. If the aberration composition of the turbulent wavefront contained higher-order aberrations, the system could not accurately measure the turbulent wavefront. When the order of the aberrations of the turbulent wavefront was low, the turbulent wavefront could be measured by the lens arrangement with fewer lens units, and the wavefront reconstruction accuracy was close to the measurement results obtained when more lens units were used.

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Condition Number as a Metric for the Effectiveness of Polarimetric Algorithms

Cited by 7 publications

References 4 publications

Polarization modeling and predictions for Daniel K. Inouye Solar Telescope part 4: calibration accuracy over field of view, retardance spatial uniformity, and achromat design sensitivity

Polarization modeling and predictions for Daniel K. Inouye Solar Telescope part 4: calibration accuracy over field of view, retardance spatial uniformity, and achromat design sensitivity

Polarization modeling and predictions for DKIST part 2: application of the Berreman calculus to spectral polarization fringes of beamsplitters and crystal retarders

Simulation Analysis of an Atmospheric Turbulence Wavefront Measurement System

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