Yao Hu

Random phase-shifting interferometry without accurately controlling or calibrating the phase shifts

A random phase-shifting interferometry insensitive to environmental noises is proposed. The relationship between intensity and phase in each pixel is obtained from a large amount of phase-shifting interferograms. In the phase-solving algorithm, the phase shift step length is not taken as a parameter, but the temporal intensity maximum and minimum in each pixel are needed. For finding the extreme values, random passive phase shifts caused by environmental noises are adopted to make the intensity ergodic. Supplementary active phase shifts, which are not accurately controlled or calibrated, are performed to shorten the measurement cycle. Finally, averaging statistically uncorrelated data over a long enough period of time can effectively reduce most random errors. A minitype Fizeau interferometer applying this random phase-shifting method demonstrated the feasibility of it.

Inverse Hartmann surface form measurement based on spherical coordinates

Various methods for surface form measurement of aspheric and complex optics exist at present. Each method is just suitable for several limited optic surface form measurement. Hartmann measurement is a method that reconstructs the surface form of a test mirror from form slope. It gives quantitative evaluation of a test mirror in a short time. Compared with interferometry, it has advantages such as relatively simple setup, good anti-disturbance property and low cost. However, it is difficult for conventional Hartmann and Shack-Hartmann methods to increase their measurement dynamic range and resolution simultaneously, and they can not be used to measure steep aspheric surface form. A novel method named inverse Hartmann surface form measurement based on spherical coordinates is presented. The method increases the measurement dynamic range and resolution simultaneously. It reduces the measured ray slope, increases the measurement range, and its accuracy of form error is higher than that in rectangular coordinates. It can be applied in online optic product evaluation rapidly and accurately with low cost.

Compensation ability evaluation of part-compensation lens based on slope asphericity

The accurate evaluation on the compensation range of part-compensation lens is beneficial to guide the design of part-compensation lens and realize fast testing on many aspheric surfaces. The prior evaluation methods based on asphericity have error judge occurred, thus reduce the compensation range of part-compensation lens negatively, further increase the testing time of aspheric surface. Therefore, an evaluation method based on slope asphericity that fits testing requirements is proposed to evaluate the compensation range of part-compensation lens. Mass simulations are processed to compare different evaluations and the effect of aspheric surface parameters on compensation range evaluation is analyzed. Additionally, the operation mechanism of part-compensation lens is analyzed from slope match of rays. The results indicate that accurate evaluation can be realized via using slope asphericity, thus is beneficial to design a part-compensation lens with the compensation range as large as possible.

A best-fit sphere definition capable of reducing dynamic range in aspheric surface testing

In order to fit the requirements of aspheric surface testing, a new best-fit sphere definition is proposed. The application and importance of the best-fit sphere definition in aspheric surface testing are analyzed. According to mass simulations, the characteristics of the best-fit sphere are analyzed, and the formulas of its sphere center and radius are given. The analysis indicates that the best-fit sphere definition is directly relative to the manufacture difficulty of CGH and the testing difficulty of aspheric surface to represent the testing difficulty of aspheric surface and reduce the testing dynamic range, and is beneficial to reduce the testing error of laser deflectometry and expand testing range.

Experimental research on anti-vibration interferometry based on time-frequency-domain analysis

Phase-shifting interferometry is a non-contact precision precise measuring method for optical surface, but it is highly sensitive to external vibrations. A time-and-frequency-domain (TFD) anti-noise phase-shifting interferometry is proposed to eliminate the effect of vibrations and improve the precision of measurement. According to simulations and preliminary experiments, active phase-shifting speed as well as interferogram capture speed should be increased to improve the anti-vibration capability of the TFD method. In this paper, a fast phase-shifting approach based on PZT actuator and interferogram detection with high-speed camera is proposed. Preliminary experimental results are given to demonstrate the approach.

Discussion on spatial spectral characteristic of Fourier transform method for interference fringe analysis

Because of the global characteristic of the Fourier transform method for fringe pattern analysis, it has been extensively developed and widely used in optical metrology. Many other works were published afterward; however, the spatial spectrum characteristic of the Fourier transform method has not been fully and systematically investigated. The spatial spectrum characteristic and its relationship with factors such as the quantization of grey levels, random noise, and spatial carrier frequency are discussed. The results indicate that, the maximum bandwidth can be measured by the Fourier transform method is close to Nyquist sampling theorem. That provides a theoretical quantitative basis for the study of extending the measurement range of the Fourier transform method, also builds the relationship between the spatial frequency can be measured and the resolution of interferogram detector.

A variable resolution feedback improving the performances of object detection and recognition

In order to improve the performances of object detection and recognition, a two-stage framework combined with variable resolution control strategy is proposed. The images in low resolution and high resolution are employed in object detection and object recognition, respectively. Meanwhile, a feedback mechanism used in two-stage framework is proved to effectively improve the performances of object detection. The results show that under low resolution, the accuracy of object detection based on fixed resolution 320 × 240 without feedback mechanism is 36.7%. However, the accuracy of object detection of the proposed method based on variable resolution increases to 95.3%. Under high resolution, compared with the method based on fixed resolution 1280 × 960 using the two-stage framework, the time consumption of the proposed method with variable resolution decreases by 51.4%, while keeping almost identical recognition accuracy.

Digital Moiré Phase-Shifting Interferometric Technique for Aspheric Testing

Faster and more accurate optical aspheric testing methods are required in many technical fields. A digital moiré phase shifting interferometer (DMPSI) with partial compensation lens (PCL) is proposed. With digital phase shifting technique, only one shot of interferogram is required, so the system structure is simpler with lower sensitivity to the environmental vibration. PCL is designed to enlarge the measurement range of asphericity. A DMPSI prototype in Fizeau configuration has been developed. After calibration, spherical surface is tested with accuracy comparable to Zygo interferometer.

Research on the key parameters influencing the anti-vibration capability of time-frequency-domain interferometer

This paper introduces a time-and-frequency-domain (TFD) anti-noise phase-shifting interferometry, and designs an experimental system to test the anti-vibration ability of this method. In the system, a plane mirror is measured under the external vibrations simulated by the standard mirror propelled by PZT. During the measurement, each of the key parameters is assigned different values. By analyzing the testing results, the law of the parameters’ influence on system anti-vibration capability can be obtained. According to the law, the optimization parameters can be determined so that the system has the maximum anti- vibration capability.

Measurement of optical glass refractive index free from effect of environmental temperature

A method based on measurement of critical refraction angle is proposed for measurement of optical glass refractive index independent of environment temperature. The critical refraction angle difference between the test sample and a standard refractive index block is measured first, and then the refractive index difference is obtained by a linear regression algorithm and the refractive index of the sample can be calculated from it. The requirement for environmental temperature is 25±5 °C , which can be easily satisfied on the production line. Compared with the non-linear algorithm used for direct measurement, this method is simpler, more efficient, and can directly get the refractive index value at standard temperature. Experimental result shows that the measurement repeatability is 1×10-5. The method can be used for fast and accurate measurement of the refractive index for the same glass material in mass production (e.g. X-cube made of K9 optical glass).