Phase error calculation in a Fizeau interferometer by Fourier expansion of the intensity profile

Dorrio, Benito Vasquez; Blanco-García, Jesús; López, Carlos Pérez; Doval, Ángel F.; Soto, R.; Fernández, José Luis Fernández; Pérez‐Amor, M.

doi:10.1364/ao.35.000061

Cited by 27 publications

(6 citation statements)

References 3 publications

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“…This is a slight modification of the Airy formula used for Fizeau interferometers [14][15][16], with an additional allowance for linear intensity drift. Here t labels camera frames and is interpreted as a time in units of phase steps, ω is the size of a phase step and thus the fringe frequency in rad/step, and ϕ 0 represents the phase of the fringe at t = 0.…”

Section: Apparatusmentioning

confidence: 99%

“…To either side of the DC peak corresponding to the average intensity, we see the fundamental fringe oscillation (± 1 on the graph's abscissa), followed by the higher harmonics associated with the deformation of the fringe. The amplitude ratio between successive harmonics, which corresponds to the geometric mean of the reflectances of the optical flat and platen [16], is…”

Section: Apparatusmentioning

confidence: 99%

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Robust phase-stepping interferometry for traceable length measurements in a Hilger–Watts gauge-block interferometer

Leroux¹,

Eves²

2020

Metrologia

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We demonstrate a simple adaptation of the venerable Hilger-Watts gauge-block interferometer capable of performing automated, traceable calibrations of gauge block length by phase-stepping interferometry (PSI). We discuss the selection of robust PSI filtering algorithms to counteract in software the flaws of the hardware implementation, including markedly non-sinusoidal fringes and inhomogeneous phase step size. We find that the length measurement errors attributable to the phase measurement can be reduced to 0.6 nm, even with a simple retrofit to an instrument not originally designed for PSI.

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Section: Apparatusmentioning

confidence: 99%

Section: Apparatusmentioning

confidence: 99%

Robust phase-stepping interferometry for traceable length measurements in a Hilger–Watts gauge-block interferometer

Leroux¹,

Eves²

2020

Metrologia

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“…Rapid, in situ gathering of the surface wave front data is needed in order to make the etch process closedloop. To realize this, we built a large aperture Fizeau interferometer, ref [5][6][7][8][9][10][11], that is capable of measuring the wave front of up to 1 m size thin sheets. A schematic of this apparatus is shown in figure 3.…”

Section: Fy02 Er Effort: Development Of 2-d Parallel Etching Toolsmentioning

confidence: 99%

Development of Wet-Etching Tools for Precision Optical Figuring

Rushford¹,

Dixit²,

Hyde³

et al. 2004

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This FY03 final report on Wet Etch Figuring involves a 2D thermal tool. Its purpose is to flatten (0.3 to 1 mm thickness) sheets of glass faster thus cheaper than conventional sub aperture tools. An array of resistors on a circuit board was used to heat acid over the glass Optical Path Difference (OPD) thick spots and at times this heating extended over the most of the glass aperture. Where the acid is heated on the glass it dissolves faster. A self-referencing interferometer measured the glass thickness, its design taking advantage of the parallel nature and thinness of these glass sheets. This measurement is used in close loop control of the heating patterns of the circuit board thus glass and acid. Only the glass and acid were to be moved to make the tool logistically simple to use in mass production. A set of 4-circuit board, covering 80x80-cm aperture was ordered, but only one 40x40-cm board was put together and tested for this report. The interferometer measurement of glass OPD was slower than needed on some glass profiles. Sometimes the interference fringes were too fine to resolve which would alias the sign of the glass thickness profile. This also caused the phase unwrapping code (FLYNN) to struggle thus run slowly at times taking hours, for a 10 inch square area. We did extensive work to improve the speed of this code. We tried many different phase unwrapping codes. Eventually running (FLYNN) on a farm of networked computers. Most of the work reported here is therefore limited to a 10-inch square aperture. Researched into fabricating a better interferometer lens from Plexiglas so to have less of the scattered light issues of Fresnel lens groves near field scattering patterns, this set the Nyquest limit. There was also a problem with the initial concept of wetting the 1737 glass on its bottom side with acid. The wetted 1737 glass developed an Achromatic AR coating, spoiling the reflection needed to see glass thickness interference fringes. In response to this dilemma, the acid wetting was moved to the top of the glass and the thermal diffusion layer under the glass replaced with rubber. The bottom side of the glass was then protected from etching with a vacuum grease layer on the glass, though many other ways were tried and need to be further developed. We switched our mission away from flattening the OPD of 1737 glass, as the Eyeglass project no longer wanted glass. We turned our attention to the NIF Borofloat Debris shields.

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“…In case of multiple-beam Fizeau system, fringes with airy profile are obtained due to the multiple reflection of the incident beam (Bonsch & Bohme, 1989). Thus evaluation of the phase values will not be accurate if two-beam phase-stepping algorithms are used (Dorrio et al, 1996). Accordingly, the digital evaluation of the phase map of multiple-beam interference fringes would be erroneous due to the nonsinusoidal nature of the fringes.…”

Section: Introductionmentioning

confidence: 99%

A novel double‐image Fizeau system for accurate investigation of anisotropic polymer fibres

Hamza

Sokkar

El‐Farahaty

et al. 2014

Journal of Microscopy

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SummaryThis paper introduces a double-image multiple-beam Fizeau fringes system. The introduced system can dynamically determine the variations of the refractive indices for both parallel and perpendicular polarization simultaneously. This is achieved by the simultaneous capturing of two multiple-beam interference patterns during the mechanical processing of isotactic polypropylene fibre. This parallel determination of the refractive indices of both polarization directions allowed us to determine the full-field distribution of the stress vector, S. To accomplish this, a mathematical model was deduced to calculate the components of the stress vector, S, i.e. parallel stress component, S 1 , and perpendicular stress component, S 2 . Double-image Fizeau fringes system and the deduced mathematical model were used to investigate the variation of the refractive index and stress components of the fibre during the stretching process and propagation of necked regions.

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Phase error calculation in a Fizeau interferometer by Fourier expansion of the intensity profile

Cited by 27 publications

References 3 publications

Robust phase-stepping interferometry for traceable length measurements in a Hilger–Watts gauge-block interferometer

Robust phase-stepping interferometry for traceable length measurements in a Hilger–Watts gauge-block interferometer

Development of Wet-Etching Tools for Precision Optical Figuring

A novel double‐image Fizeau system for accurate investigation of anisotropic polymer fibres

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