Phase shifting technique using generalization of Carre algorithm with many images

Magalhães, Pedro Américo Almeida; Neto, Perrin Smith; Barcellos, Clóvis Sperb de

doi:10.1007/s10043-009-0083-7

Cited by 13 publications

(3 citation statements)

References 7 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…According to the average coefficients a and b derived from table 1, the humidity correction equation is deduced in equation (11).…”

Section: Experiments and Resultsmentioning

confidence: 99%

“…where subscript t represents experiment temperature, subscript i represents different laser wavelength (532 nm, 633 nm, 780 nm), λ i t 0, is the laser wavelength in vacuum, N i t , is integer of the interference order which can be calculated by equation (5) according to the rough length of the sample, ε i t , is fraction of the interference order which can be acquired through 4-step phase shifting as followed [11]: , varies while the integer N i t , keeps invariant in spite of large temperature change during the whole experiment. The sample length variation doesn't exceed a wavelength accordingly.…”

Section: Principlementioning

confidence: 99%

See 1 more Smart Citation

Revision to the humidity correction equation in the calculation formulae of the air refractive index based on a phase step interferometer with three frequency-stabilized lasers

Qianghua¹,

Zhang²,

Liu³

et al. 2016

Meas. Sci. Technol.

View full text Add to dashboard Cite

At present the formulae proposed by G Boensch and E Potulski in 1998 (Boensch and Potulski 1998 Metrologia 35 133–9) are mostly used to calculate the air refractive index. However, the humidity correction equation in the formulae is derived by using the light source of a Cd lamp whose light frequency stability is poor and at a narrow temperature range, around 20 °C. So it is no longer suitable in present optical precision measurements. To solve this problem, we propose a refractive index measurement system based on phase step interferometer with three frequency stabilized lasers (532 nm, 633 nm, 780 nm), corrected coefficients of the humidity are measured and a corresponding revised humidity correction equation is acquired. Meanwhile, the application temperature range is extended from 14.6 °C to 25.0 °C. The experiment comparison results at the temperature of 22.2–23.2 °C show the accuracy by the presented equation is better than that of Boensch and Potulski.

show abstract

“…According to the average coefficients a and b derived from table 1, the humidity correction equation is deduced in equation (11).…”

Section: Experiments and Resultsmentioning

confidence: 99%

Section: Principlementioning

confidence: 99%

Revision to the humidity correction equation in the calculation formulae of the air refractive index based on a phase step interferometer with three frequency-stabilized lasers

Qianghua¹,

Zhang²,

Liu³

et al. 2016

Meas. Sci. Technol.

View full text Add to dashboard Cite

show abstract

“…Unfortunately, in cases where the noise is important, the algorithm will fail to fulfil the task of measuring [10]. Recently, a modified Carré algorithm [11] has been proposed to minimize the uncertainty due to errors and 3 Author to whom any correspondence should be addressed. random noise effects in the images during the computation of phase step from the interferometric patterns.…”

Section: Introductionmentioning

confidence: 99%

Algorithm for phase shifting shadow moiré with an unknown relative step

Du¹,

Zhao²,

Li³

et al. 2011

J. Opt.

View full text Add to dashboard Cite

We report our experimental results of phase shifting shadow moiré with a constant but unknown phase step to estimate both the wavefront phases and the phase step. The method allows phase retrieval from phase shifting interferograms even though the calibration data of the phase shifter are unknown. Compared with the traditional shifting shadow moiré method, the proposed algorithm is insensitive to the height dependent effects, which is the main systematic source of error in phase shift shadow moiré when reconstructing surfaces from fringe patterns. Experiments show that the proposed method can effectively minimize the effects of the phase shifting errors and possesses a superior performance to existing typical phase shifting algorithms in the shifting shadow moiré technique.

show abstract