Deflectometry is a metrology method able to measure large surface slope ranges that can achieve surface reconstruction accuracy similar to interferometry, making it ideal for freeform metrology. While it is a non-null method, deflectometry previously required a precise model of the unit under test to accurately reconstruct the surface. However, there are times when no such model exists, such as during the grinding phase of an optic. We developed a model-free iterative data processing technique which provides improved deflectometry surface reconstruction of optics when the correct surface model is unknown. The new method iteratively reconstructs the optical surface, leading to a reduction in error in the final reconstructed surface. Software simulations measuring the theoretical performance limitations of the model-free processing technique as well as a real-world test characterizing actual performance were performed. The method was implemented in a deflectometry system and a highly freeform surface was measured and reconstructed using both the iterative technique and a traditional non-iterative technique. The results were compared to a commercial interferometric measurement of the optic. The reconstructed surface departure from interferometric results was reduced from 44.39 μm RMS with traditional non-iterative deflectometry down to 5.20 μm RMS with the model-free technique reported.
A segmented mirror is one of the most promising solutions to build an extremely large aperture telescope to reveal the secrets of the universe. In this manuscript, we present a simultaneous angle alignment method for segmented mirrors. By taking the displayed sinusoidal pattern reflecting off the mirrors, the tip-tilt angles are measured with 0.8 μrad resolution for a flat mirror. Due to the efficient calculation using Fourier analysis, the total measurement time for seven flat mirrors is 0.07 s. In addition, a multiplexed sinusoidal pattern is adapted to resolve the intrinsic 2π ambiguity problem in a sinusoidal signal. The presented method can measure any number of segmented mirrors provided that the camera’s field of view can cover them all simultaneously.
Dynamic metrology holds the key to overcoming several challenging limitations of conventional optical metrology, especially with regards to precision freeform optical elements. We present two dynamic metrology systems: 1) adaptive interferometric null testing; and 2) instantaneous phase shifting deflectometry, along with an overview of a gradient data processing and surface reconstruction technique. The adaptive null testing method, utilizing a deformable mirror, adopts a stochastic parallel gradient descent search algorithm in order to dynamically create a null testing condition for unknown freeform optics. The single-shot deflectometry system implemented on an iPhone uses a multiplexed display pattern to enable dynamic measurements of time-varying optical components or optics in vibration. Experimental data, measurement accuracy / precision, and data processing algorithms are discussed.
Freeform optics provide excellent performance for a wide variety of applications. However, obtaining an accurate freeform surface measurement is highly challenging due to its large aspheric/freeform departure. It has been proven that SCOTS (Software Configurable Optical Test System), an advanced deflectometry system developed at the University of Arizona, can measure the departure of a freeform surface from the desired shape with nanometer accuracy. Here, a new data processing technique was used to measure a freeform surface without any prior knowledge of the shape of the surface. Knowing only the geometry of one point on the test surface, this method can take a blind measurement of a freeform surface and arrive at the true surface through iterative construction.
A simple method for planar mirror pendulum pose measurement is proposed. The method only needs a LCD screen and a CCD camera. LCD screen displays calibration patterns, and the virtual images (VIs) reflected by mirror are taken by the CCD camera. By camera calibration, the pose relationships between camera and VI coordinate systems can be determined. Thus the pendulum poses of the mirror is obtained according to coordinate transition and reflection principle. This method is simple and convenient, and has a big application potential in mirror pendulum pose measurement.
A method for the optical surface defects inspection based on fringe reflection is studied. The test system is composed of
the fringe screen (a liquid crystal display, LCD), CCD camera and a computer. The intensity-modulated patterns are
generated on the screens on both the horizontal and vertical directions respectively. The CCD records the pattern images
via the tested surface. The phase and amplitude modulation are calculated by the phase-shifting technique. The defects
location can be got from the amplitude modulation. Also the height of the defects can be gained by integration from the
phase change caused by the defects. This method is simple and cheap. Compared with other techniques, this technique
can get the three dimension information of the defects. The experimental results have confirmed the feasibility of this
Three typical calibration patterns, including checkerboard, Gaussian point grid, and crossed fringe patterns, are chosen to find a good one for camera calibration. Through computer simulation and camera intrinsic parameter calibration experiment, the crossed sine fringe pattern using fringe analysis method is defined as the one with the best precision. However, the phase information is obtained by Fourier transform (FT), which cannot detect the points located in the edge of the point grid. Thus, an innovative method uses phase shifting in the fringe analysis process is proposed, it can avoid the extraction misplacement in the edge of the point grid by the FT method, and make the crossed sine fringe pattern more usable in camera calibration. The camera extrinsic parameter calibration experiment proves the effectiveness of the recent method.
We have provided a comparative analysis of methods that involves multi-angle averaging, pseudo
multi-angle averaging, single-rotation and variants based on the combinations. All these methods
require measurement results being determined at rotational positions, serving for the interferometric
measurement of rotationally asymmetric surface deviation of a specimen. Zernike coefficients and
power spectral density (PSD) are computed and used for detailed comparison. The experimental results
show that single-rotation method gives noticeably smoother result, thus it is limited to applications of
measuring low spatial frequency deviations, taking the advantage of quick measurement time with
fairly accurate rms results and potentially less influence of environment; in contrast, the result with
multi-angle averaging contains more information of mid and high spatial frequency but it’s
time-consuming. The pseudo multi-averaging method is the concise variant with fewer measurements.
Its result contains more noise errors depending on the number of rotational measurements of
Laser interferometry measurement using the volatility of light, with the advantages on high resolution, high accuracy,
high sensitivity and reproducibility, it has become the primary means of the optical shape measurement. Laser
wavelength scanning interference moves the test aspheric mirror in the optical axis direction controlled by the electric
translation stage precisely, gradually changes the relative distance between the aspheric test mirror and the interferometer.
Thus the reference sphere wavefronts with different radius match automatically to different ring-zones of the aspheric
mirror. Based on the laser wavelength scanning interference testing of aspheric surface, this paper calculates the center
area and the annular area separately. In the annular area processing, the authors use Zernike polynomials to fit the phase
diagram, then derivative along the radial direction, to extract the zero-phase points on the interferogram of each relative
position, and get the angle between the normal and the aspheric axis, then rebuild the absolute position of the coordinate
system of aspheric mirror. Experimental results show that the method has high accuracy and reliability.
A method based on basic phase measuring deflectometry is proposed for testing the aspherical mirror. The method uses a reference screen in two different distances from the mirror under test. The sinusoidal, intensity-modulated patterns generated by the computer are displayed on the LCD screen, and the camera observes the patterns reflected off the testing mirror. The observed pattern appears distorted depending on the shape of the mirror. Using the phase-shifting technique, the original ray of every image point and its corresponding deflected ray can be constructed. Their intersection points and the surface normal are obtained. Then the mirror surface is reconstructed with high accuracy by numerically integrating the surface normals. The proposed method is robust against noise and can test the mirror full field. In this work, the method is introduced, and computer simulation and experimental results are shown.