Experimental studies of compact soft X-ray sources (wavelength 1 Å < λ < 50 Å) often require obtaining a two-dimensional image of the source with high spatial resolution. The simplest instrument for obtaining such an image is a pinhole, which consists of a small-size orifice in a material opaque to the radiation.  When the X-ray source has low intensity, the pinhole diameter may be increased to obtain a reliably detectable image on the detector. However, thereby the spatial resolution at the object reduces. In this paper, we propose the method for improving the spatial resolution of images recorded using large-aperture (i.e. enable high radiation pass through ability) pinholes. The method is an image reconstruction with a mathematical procedure based on a solution of an ill-posed problem – the Fredholm integral equation of the 1st kind – with an iteration algorithm. This algorithm is known as the minimization of directed divergences or the maximum likelihood. For our purpose, we have created a special instrumental function and modified the algorithm for its application to the reconstruction of images recorded with large-aperture pinholes and developed the appropriate software.

Model experiments and reconstructions of images obtained in actual experiments with electric-discharge sources have demonstrated the high efficiency of the proposed iteration method for improving (by few times) the spatial resolution of images recorded by large-aperture pinholes. Thus, the reconstructed images have a spatial resolution significantly better than the native geometric resolution of these pinholes. Figure 1 presents the result of a model experiment on reconstructing the image of two closely spaced point sources to demonstrate the efficiency of the developed method.

Proposed approach has implemented to use large-aperture pinholes in experimental diagnostics for studying low-intensity, small-scale emitting objects. These pinholes are simple to fabricate and possess high radiation pass through ability, but previously they were generally not used due to their inherently low geometric spatial resolution.

Fig. 1. Image of the model source (consisting of two closely located point sources) recorded through the large‑aperture pinhole (a). The image of this model source reconstructed using the developed method with the special instrumental function (b). Pixel numbers are plotted along the coordinate axes. The color scale corresponds to intensity gradations.

Evgeny Bolkhovitinov et al.,
JETP Letters 124, issue 7 (2026)