Wavefront aberration measurements are required to test an extreme ultraviolet (EUV) imaging system. For a high-NA EUV imaging system, where conventional wavefront-sensing techniques show limitations, ptychography can be used for this purpose. However, at the wavelength region of EUV (i.e., 13.5 nm), the position accuracy of the scanning mask that is defined for ptychography is stringent. Therefore, we propose ptychography combined with mask position correction. The simulated intensity patterns, the ones we use, resemble expected EUV experimental data. Finally, we show the results in the presence of Poisson noise and the tolerance of the position correction method for error in mask positions.@en

Lenses are indispensable tool to perform imaging and see the small details of an object which was otherwise not possible. The smallest feature of an object that one can see using a lens depends on the numerical aperture (NA) of the lens and the used wavelength of light. For a fixed NA, the shorter the wavelength is, the smaller the features of an object can be seen. Therefore, for high-resolution imaging, short wavelengths such as x-rays and e-beams are used. For these wavelengths, the refractive index of the most of the materials is close to 1. Therefore, rays passing through these lenses do not deviate and get absorbed within the materials eventually. To circumvent this problem, different types of diffractive lenses were introduced. Imaging can be performed using these lenses, however, it cannot achieve diffraction limited resolution. The reason for this is the present aberrations in the imaging systems. To this end, computational imaging methods start to play a major role. Lensless imaging is a type of computational imaging which replaces a lens by algorithms. Hence, lensless imaging is not limited by the present aberrations of the lens or imaging system. Besides, with this technique not only amplitude but also phase information can be retrieved. Phase information is important especially for low contrast objects. Since these algorithms solve the phase of the object iteratively, they are also called as phase retrieval techniques. In the past, several phase retrieval techniques were proposed. Some techniques are successful and some techniques have achieved limited success. For the last few decades, ptychography has been evolving dramatically. Ptychography has been found to be more robust than other existing phase retrieval method, and it has shown potential to be implemented for x-rays and e-beams wavelengths. Ptychographic data is so rich in information that not only it retrieves the object function but also it can retrieve the probe function, 3D information of the object, coherent modes of the light, etc. Ptychography is a phase retrieval technique which uses several far-field diffraction patterns of an object. These patterns are created by scanning the object sequentially using an illuminated probe. The probe position should be in a way that neighboring probes overlap with each other. Due to this overlap area, the ptychographic data contains redundancy and this helps the algorithm to converge fast. When ptychography was implemented using e-beam, the reconstructions suffered from the required accuracy of initial parameters. For instance, 50 pm of accuracy is required in probe positions which is difficult to achieve. This high demand in accuracy undermined its applicability to short wavelengths. Therefore, several attempts were made to correct probe positions in ptychography...@en

Ptychography is a form of coherent diffractive imaging; it employs far-field intensity patterns of the object to reconstruct the object. In ptychography, an important limiting factor for the reconstructed image quality is the uncertainty in the probe positions. Here, we propose a new approach which uses the hybrid input-output algorithm and cross-correlation in a way that can correct our estimates of the probe positions. The performance and limitations of the method in the presence of noise, varying overlap, and maximum recoverable error are studied using simulations. A brief comparison with other existing methods is also discussed here.

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We have demonstrated that the extended ptychographic iterative engine (ePIE) algorithm can be applied to retrieve the phase information of the vectorial scattered field of a subwavelength object with the amplitude of the scattered field as input. We applied this technique combined with coherent Fourier scatterometry to determine the phase of the scattered field of a subwavelength grating, illuminated by a focused laser beam.

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X-rays and e-beams are used for high-resolution imaging where the requirement for highly accurate lenses is one of the limiting factors. Hence, lensless imaging is preferred. Coherent Diffractive Imaging (CDI) is a lensless imaging technique which uses intensity patterns in the far-field to obtain the complex amplitude of the object. Ptychography, an emerging area of research, belongs to the class of CDI techniques. In ptychography, the object is partially illuminated by a scanning probe and the intensity patterns in the far-field for each probe position are recorded and used to reconstruct the object. One of the important aspects to the success of this method is the overlap between the adjacent probes and the accurate knowledge of the probe positions. Recently, we proposed a new method to correct the probe positions which uses the gradient of intensity patterns in the far-field. Here, we propose another method to correct probe positions.

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Ptychography, a form of Coherent Diffractive Imaging, is used with short wavelengths (e.g. X-rays, electron beams) to achieve high-resolution image reconstructions. One of the limiting factors for the reconstruction quality is the accurate knowledge of the illumination probe positions. Recently, many advances have been made to relax the requirement for the probe positions accuracy. Here, we analyse and demonstrate a straightforward approach that can be used to correct the probe positions with sub-pixel accuracy. Simulations and experimental results with visible light are presented in this work.

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For high resolution imaging, X-rays and electron beams are being used. However, for such a short wavelength, imaging with lenses becomes difficult as lenses absorb a part of radiation and lenses with very low aberrations must be used. Ptychography is a lens-less imaging technique which uses intensity information of the multiple diffraction patterns in the far field. These multiple far field diffraction patterns are generated by an unknown object which is scanned by a localized illuminated spot (probe). Accurate knowledge of initial parameters is important for a good reconstruction of the object. Robustness of the Ptychography Iterative Engine (PIE) has already been studied for inaccurately known initial parameters, where the success of the algorithm was found to be sensitive to the accuracy of the estimate of lateral positions of the probe.:; We present here a new method to correct the lateral position of the probe with respect to the object. This method is more straightforward to implement than other existing algorithms while comparable accuracy for the lateral position is achieved. Being able to correct the probe positions has positive implication in experiments, in particular at the short wavelength cases. It relaxes the requirement for the experimental set-up.@en