| Point diffraction interferometer （PDI） uses the diffracted wavefront from anoptical fiber or a pinhole as the reference, which is a nearly ideal spherical wavefront.It has high accuracy and can provide testing services for EUV projection systems’development. In practical applications, to obtain a high accuracy criterion wavefrontis one of the key parts of developing a PDI. Therefore, it is important to evaluate thequality of diffracted criterion wavefront. At present, there are two methods: one isbased on numerical simulation; the other is the shearing interferometry by using twosimilar diffracted beams to evaluate the quality of the criterion wavefront indirectly.The first method can provide some theoretical data for the development of PDI. Thesecond one can evaluate the criterion wavefront practically. However, this methodsuffers from high frequency noise. Meanwhile, based on the identity between the twoshearing wavefront, the differences between the two shearing beams will affect theresult in the practical case. Therefore, a direct method of evaluating the diffractedcriterion wavefront needs to be studied. It can provide a technical support for both theassessment of aberrations in the diffracted criterion wavefront and the alignment ofPDI. Phase retrieval method is a direct testing method, the aberrations can be obtainedbased on the acquired star images. This method can be applied in the evaluation of thediffracted criterion wavefront in PDI, in order to obtain the aberrations in thediffracted wavefront.This paper mainly aims at evaluating the aberrations in the criterion wavefront ofPDI, including studying on the phase retrieval algorithm, accuracy analysis, study onthe system error calibration method, and some confirmatory experimental analysis ofthe relevant testing. The main contents are as follows: 1. A mathematical model of the diffracted wavefront from a small aperture isstudied, and the functional relationship between the diffraction intensity and thediffracted wavefront is established. To evaluate the diffracted criterion wavefront inPDI using the phase retrieval technique, the mathematical relationship between thediffraction image and the diffracted wavefront is necessary. Based on the ExtendedNijboer-Zernike theory, the mathematical relationship between the diffractionintensity from a small aperture and the diffracted wavefront is analyzed and obtained.A mathematical model is established for the study on phase extraction algorithm forevaluating the diffracted criterion wavefront.2. Phase extraction algorithms for evaluating the criterion wavefront in PDI areestablished. According to the functional relationship between diffracted intensity andthe diffracted wavefront, the phase retrieval technique can be applied for the phaseextraction and evaluation of the diffracted wavefront. In order to satisfy therequirement of the high accuracy, proper phase extraction algorithms need to bedeveloped for evaluating the aberrations in the diffracted criterion wavefront. Amulti-defocus phase extraction algorithm through capturing symmetricalmulti-defocus diffraction images with an optical amplification system is designed andestablished. In addition, a single-defocus phase extraction algorithm, which canevaluate the aberrations based on one defocus diffraction intensity pattern, is proposed,in order to restrain disturbances in the testing environment and simplify the testingprocess.3. The error sources in the evaluation process of diffracted criterion wavefrontare studied, and the accuracy of the phase extraction algorithms is analyzed. Thedeveloped phase extraction algorithms have ultra-high accuracy in the ideal case. Butthese suffer from some factors in the actual testing process, such as: mechanicalpositioning errors, power instability of the light source, frequency instability inwavelength, noises in the detector, the sampling rate, veiling glare in background, andso on. Through analyzing these factors, the prediction accuracy can be estimated, andthe accuracy of multi-defocus and single-defocus phase extraction algorithms canreach the accuracy of0.026nm RMS and0.024nm RMS, respectively. It is possibleto satisfy testing requirements of the diffracted criterion wavefront.4. A calibration method is developed to correct the system errors in theevaluation process of the diffracted criterion wavefront, and the accuracy has beenanalyzed. The diffracted intensity patterns are imaged onto detectors through an optical amplification system. In order to reach such high accuracy, a calibrationmethod for correcting the systematic errors in the evaluation process of diffractedwavefront by using the phase retrieval technique is developed, and the accuracy ofthis method is analyzed. The result indicates that the theoretical accuracy can achieve2.02×10-4nm RMS.5. The experimental study is implemented by testing the diffracted wavefront.The device for testing the diffracted wavefront from a fiber was designed and built.Through the experiment, the results verified this testing method which is based on thephase retrieval technique.6. The experimental study is implemented by testing the wavefront in an opticalimaging system. Due to the high testing accuracy of the phase extraction algorithms,testing the wavefront in the optical systems with high-precision （for example:lithographic projection exposure system） based on these algorithms has a brightprospect. Building a testing device, an optical system with high-precision was tested.The difference between the retrieval result and the interferometric result of a Fizeauinterferometer was0.0074λ RMS （λ=632.8nm）. According to the result in asimulation analysis, the main error source in the testing process is the low samplingrate in capturing images. It is possible to obtain higher accuracy by means ofimproving the sampling rate. |
