The subaperture stitching interferometry is a technique suitable for testing high numerical-aperture optics, large-diameter spherical lenses and aspheric optics. In the stitching process, each subaperture has to be placed at its correct position in a global coordinate, and the positioning precision would affect the accuracy of stitching result. However, the mechanical limitations in the alignment process as well as vibrations during the measurement would induce inevitable subaperture position uncertainties. In our previous study, a rotational scanning subaperture stitching interferometer has been constructed. This paper provides an iterative algorithm to correct the subaperture position without altering the interferometer configuration. Each subaperture is first placed at its geometric position estimated according to the F number of reference lens, the measurement zenithal angle and the number of pixels along the width of subaperture. By using the concept of differentiation, a shift compensator along the radial direction of the global coordinate is added into the stitching algorithm. The algorithm includes two kinds of compensators: one for the geometric null with four compensators of piston, two directional tilts and defocus, and the other for the position correction with the shift compensator. These compensators are computed iteratively to minimize the phase differences in the overlapped regions of subapertures in a least-squares sense. The simulation results demonstrate that the proposed method works to the position accuracy of 0.001 pixels for both the single-ring and multiple-ring configurations. Experimental verifications with the single-ring and multiple-ring data also show the effectiveness of the algorithm.
Fizeau interferometer is widely used to test the surface deformation of the optical lens surface profile. However, in some
measurement circumstances the common path condition of the Fizeau configuration does not hold. For example, the subaperture
scanning interferometry of asphere or the non-null aspherical element testing has dense fringe spacing.
Systematic aberrations of non-null testing are introduced into the measurement wavefront with the high wavefront slope
of the returning beam. We propose to use a two-dimension scanning device to drive a test ball to different fields of the
Fizeau interferometer for the the interference phase at each field. By least square fitting the measurement, we can get the
double Zernike polynomial coefficients representing the field dependent aberrations in the interferometer system.
According to the coefficients, the off-axis aberrations in the interferometer can be identified
Sub-aperture testing methods are widely used in optical shops to test surface deformations of large diameter, high
numerical aperture, or aspherical lens surfaces. We are proposing a novel 4 axis vibration modulated interferometer for
subaperture testing. This interferometer takes advantage of the rotationally symmetric property of the optical lens and
measures the lens surface against its symmetry axis rotationally. By adapting a synchronous random phase modulation
measurement, interferometric data is acquired on the fly when the lens is being rotated. The vibration modulated
interference phase is then calculated and stitched into a complete lens surface map by least squared fitting. This method
has advantages over the prior methods in that it acquires the interferogram in a much shorter acquisition time, even with
lower requirements on the optics and mechanical hardware. The stitch error is then significantly decreased by increasing
both the lateral resolution of sub-aperture and the reduced position uncertainty of the stitched sub-aperture phase maps.
A measurement on a mild asphere is demonstrated to prove the feasibility of the proposed interferometer.
An aspheric testing system based on subaperture stitching interferometry has been developed. A procedure involving
subaperture aberration compensation and radial position scanning was established to resolve discrepancies in the
overlapped regions. During the aspheric measuring process, the Fizeau-interferometer axis, the optical axis of the
asphere, and the mechanical rotation axis have to be aligned. Due to the tolerance of alignment mechanisms, subaperture
interferograms would be contaminated by various amounts of aberrations associated with the rotation angle. These
aberrations introduce large inconsistencies between adjacent subapertures in the stitching algorithm. Zernike coefficients
of the subapertures in one annulus were examined and each coefficient term was found to be a sinusoidal function of the
rotation angle. To eliminate the influence of misalignments, each subaperture was compensated with appropriate
amounts of coma and astigmatism to make the resulting Zernike coefficients converge to the mean values of the
sinusoidal functions. In addition, the determination of the overlapped regions relies on the precise estimate of the
distance between the center of each subaperture and the center of the aspheric optics. This distance was first provided by
the encoder and then estimated by position scanning along the radial direction pixel-by-pixel in numerical computations.
The means of the standard deviation in the overlapped regions in the simulation and the experimental measurement of an
aspheric lens were 0.00004 and 0.06 waves, respectively. This demonstrates the reliability of the subaperture aberration
compensation and position scanning process.
A subaperture stitching algorithm was developed for testing aspheric surfaces. The full aperture was divided into one
central circular region plus several partially-overlapping annuli. Each annulus was composed of partially-overlapping
circular subapertures. The phase map in each subaperture was obtained through the phase-shifting interferometry and
retrieved by an iterative tilt-immune phase-shifting algorithm and a Zernike-polynomial-based phase-unwrapping
process. All subapertures in one annulus were stitched simultaneously in least-squares sense. By eliminating the
relative piston and tilt between adjacent subapertures, the sum of squared errors in the overlapped regions was
minimized. The phase stitching between annuli also utilized the least-squares method in the overlapped region.
Simulation results on a test wavefront with 30-wave spherical aberrations demonstrated the effectiveness of the proposed
algorithm. The rms phase residue after the phase-shifting, phase-unwrapping and phase-stitching processes was 0.006
waves, which met the precision requirement of common interferometers. This algorithm should be applicable to general
surfaces in subaperture stitching interferometry.