Evaluation of the pitch deviation of a linear scale based on a self-calibration method with a Fizeau interferometer

Abstract

A self-calibration method, in which the wavefronts of zeroth and first-order diffracted beams from a scale grating measured by a Fizeau interferometer are employed, is applied for the evaluation of the pitch deviation of a reflective-type linear scale with a grating pitch of 2.048 μm used in a commercial interferential scanning-type optical linear encoder. One of the advantages of the self-calibration method is that the pitch deviation of a scale grating can be evaluated while measuring the out-of-flatness of the scale grating under inspection and the Z-directional out-of-flatness (surface profile) of the reference optical flat in the Fizeau interferometer. Meanwhile, in a practical case, the self-calibration method is valid under the condition where the out-of-flatness of the scale grating is on the same order or less than that of the reference optical flat in the Fizeau interferometer. In this paper, theoretical analysis and numerical calculations are thus carried out to investigate the influence of the out-of-flatness of the scale grating on measurement of the pitch deviation and the out-of-flatness of the reference optical flat. Some experiments with a linear scale from a commercial interferential scanning-type linear encoder are also carried out to verify the feasibility of the self-calibration method for the evaluation of the pitch deviation of the scale having an out-of-flatness of approximately 600 nm over the analyzed area.

Self-calibration of a variable-line-spacing grating for an absolute optical encoder with a Fizeau interferometer

“…It should be noted that the influence of the out-of-flatness of a grating under test can also be included in the observed phase shifts; it can be cancelled by the arithmetic operation with the wavefront data of the positive and negative first-order diffracted beams [37]. This arithmetic operation also gives the selfcalibration characteristic to the measurement since the influence of the out-of-flatness of the reference flat can also be removed [40].…”

“…It should be noted that, in the method, the influence of the out-of-flatness error of the grating can be cancelled by the arithmetic operation with the wavefront data of the positive and negative diffracted beams [37]. A further investigation of the method has also revealed that the self-calibration of the out-of-flatness of the reference flat in a Fizeau interferometer can also be realized by using the wavefront data of the zeroth-and positive and negative firstorder diffracted beams [40]. Meanwhile, this method has not been applied to the evaluation of a VLS planar scale grating so far.…”

Self-Calibration of a Large-Scale Variable-Line-Spacing Grating for an Absolute Optical Encoder by Differencing Spatially Shifted Phase Maps from a Fizeau Interferometer

“…The authors’ group has proposed a self-calibration method, in which the pitch deviation of a standard grating can be evaluated while self-calibrating the out-of-flatness of the reference flat in a Fizeau interferometer. In the method, the pitch deviation of the grating can be readily evaluated by using the wavefronts of the first-order diffracted beams from a grating [ 24 , 25 ]. The self-calibration method has been further extended to evaluate the pitch distribution of a VLS grating by linking the VLS parameters with the differential wavefronts of the first-order diffracted beams through a simple polynomial fitting process [ 26 ].…”

A Self-Calibration Stitching Method for Pitch Deviation Evaluation of a Long-Range Linear Scale by Using a Fizeau Interferometer

“…In responding to the above issues, an interferometric calibration method has been proposed to evaluate the pitch deviation of the scale grating using a Fizeau form interferometer through wavefront analysis [16]. The proposed method is further improved to a self-calibration method so that the influence of the reference flat error in the Fizeau interferometer can be removed [17][18][19].…”