A method for iterative formation of an image of a specimen to be studied in a particle-optical apparatus on the basis of a series of experimental images (the experimental series), each of which is recorded with a respective different value of at least one imaging parameter, which method comprises the steps of:
- a) determining a simulation of the illuminating particle wave directly behind the specimen (the specimen wave);
- b) determination of an estimation of a series of images of the specimen (the estimated series), in which series said imaging parameter has each time said respective different value, said determination being executed by processing in the frequency domain on said simulation of the specimen wave while utilizing a function of the particle-optical apparatus, which function represents transfer properties in the frequency domain of the apparatus;
- c) forming respective differences between the estimation of said images and corresponding experimental images of the specimen to be studied;
- d) carrying out a test as to whether said differences satisfy a predetermined approximation criterion, which test may have a first or a second test result;
- e) first forming sub-correction waves, in dependence on the first test result, by executing in the frequency domain, for each image of the series of images, an operation on said difference while utilizing the function of the particle-optical apparatus which is associated with said image and which represents the transfer properties in the frequency domain of the apparatus, and subsequently forming a correction wave by addition of the individual sub-correction waves and the subsequent correction of the simulation of the specimen wave by means of the correction wave thus obtained;
- f) repeating the above steps a) to e) in dependence on the first test result;
- g) terminating the iterative operation in dependence on the second test result;
- wherein in each iteration step of the iterative operation for each image I.sub.n (R) of the experimental series:
- the function of the particle-optical apparatus representing transfer properties in the frequency domain (G) of the apparatus is formed by the transfer function p.sub.n (G) of the apparatus;
- a set of such transfer functions is defined, each item p.sub.n,i (G) of the set corresponding to a respective different set of values of imaging parameters leading to incoherence;
- a set of sub-image waves .psi..sub.n,i (R) is formed in real space by multiplying said simulation of the specimen wave .phi.(G) in the frequency domain (G) by each time a different item p.sub.n,i (G) of the set of transfer functions, and by subjecting the product .psi..sub.n,i (G) to an inverse Fourier transformation;
- in which during the estimation
- a set of sub-images I.sub.n,i (R) is formed at the area of the detector in the real space (R) from the modulus squared of each of said sub-image waves .vertline..psi..sub.n,i (R).vertline..sup.2 in the real space (R), and the estimation of each item I.sub.n (R) of the estimated series is formed as the weighted sum .SIGMA..sub.i g.sub.i I.sub.n,i (R) of the sub-images I.sub.n,i (R) with a weighting factor g.sub.i obtained from the spread of said imaging parameters leading to incoherence;
- a series of difference images .DELTA.I.sub.n (R) is formed by subtracting the estimation of each item of the series of images I.sub.n (R) at the area of the detector from the corresponding item of the experimental series;
- each item of the series of difference images .DELTA.I.sub.n (R) is multiplied by an associated item of the set of sub-image waves .psi..sub.n,i (R) in the real space, after which the product thus formed is subjected to a Fourier transformation;
- a set of intermediate products is obtained by multiplying each item of the series of the products FT{.DELTA.I.sub.n (R).times..psi..sub.n,i (R)} thus Fourier transformed by the complex conjugate of an associated item p.sub.n,i (G) of the set of transfer functions;
- each sub-correction wave .DELTA..phi..sub.n (G) is formed as the weighted sum .SIGMA..sub.i g.sub.i .times.p*.sub.n,i (G).times.FT{.DELTA.I.sub.n (R).times..psi..sub.n,i (R)} of intermediate products with the weighting factor g.sub.i obtained from the spread of said imaging parameters leading to incoherence.