&lt;title&gt;Transfer function characterization of laser Fizeau interferometer for high-spatial-frequency phase measurements&lt;/title&gt;

LIL and LMJ are two French high power laser facilities dedicated to laser-plasma interaction experiments. In order to control the flatness requirements of their optics in a wide spatial periods bandwidth, the CEA has several Fizeau interferometers of different diameters. We use special phase objects to qualify their spatial resolutions. A few papers already dealt with the determination of a Fizeau interferometer transfer function. This was achieved by using either a phase step object or a "virtual" sinusoidal phase object (made of the superposition of two wavefronts with different amplitudes and a small tilt). For practical reasons, we chose to use true sinusoidal phase objects to qualify our instruments. Sinusoidal profiles were then eroded in silica plates. Three different periods are available: 10 mm, 2.5 mm and 1 mm, with two different amplitudes for each period. These phase plates are used to qualify the interferometers performance in terms of spatial resolution in the different configurations (wide or narrow field of view, reflection or transmission) used for LIL/LMJ optics inspection. A comparison to the transfer functions obtained using steps of different widths is also proposed. An experimental verification of the Talbot effect is achieved with the 1-mm plate to investigate propagation effects, as well as contribution of the depth of field.

Section: Methodsmentioning

confidence: 99%

Using phase objects to qualify the transfer function of Fizeau interferometers for high spatial frequencies

Bouillet

Daurios

2007

“…The focal length of the f/6 collimator is about 600mm, which is folded by two pairs of mirrors to reduce the length of the interferometer. The System transfer function (STF) of the interferometer calculated by measuring a high quality phase step [2,3] is presented in Figure 2.It shows that the STF remains higher than 0.6 at spatial frequency less than2.49line/mm. …”

Section: Coherent Optical Interferometic System Designmentioning

confidence: 97%

Design of a coherent optical interferometric system

Jia-dong¹,

Sheng²,

Chai³

et al. 2006

A 100-mm-aperture high lateral resolution interferometer has been developed in Fine Optical Engineering Research Center (FOERC), which is applied to the measurement of spatial frequencies of up to 2.5lines/mm over a 100mm field of view. The system transfer function of the interferometer is greater than 60% at near half the Nyquist frequency .To demonstrate the performance o f this high lateral resolution interferometer, theoretical errors of the system are thoroughly analyzed and the design implementation is carefully studied, such as light source, wave front slope, tolerance analysis, CCD sample and so on.

“…The phase step is widely used to test the system transfer function of the interferometer by comparing the measured Power Spectral Density Function (PSD) of a step with those from a mathematically generated ideal step [5] . The PSD of a step of height H, measured with N data points over distance L is approximately:…”

Section: Phase Stepmentioning

confidence: 99%

“…A useful way to characterize such small-scale surface irregularities is by their spatial frequency power spectrum, which can be derived from surface profiles obtained by interferometric measurements [5] . However, to obtain reliable values of the spatial frequency power spectrum of irregularities with very small amplitudes over a wide range of spatial frequencies, it is essential to avoid two major sources of errors.…”

Section: Introductionmentioning

confidence: 99%

Interferometric measurements of mid-spatial scale surface irregularities

Xu¹,

Xu²,

Chai³

et al. 2007

A simple method which can be used to map mid-spatial scale surface irregularities with high signal noise ratio is described. Two major sources of errors are analyzed and removed. One is the contributions of small-scale irregularities of the reference surface, which are subtracted by shifting the test surface laterally by a distance.The other is the spurious response of CCD, which is removed by interpolation function. The presented method is verified by simulations and experiments. It shows that it can measure mid-spatial scale surface irregularities exactly and smaller scale surface irregularities can be obtained by making measurement for a series of the lateral shifting values corresponding to one-half of the pixel space on CCD.