Objective: A new auto-focusing function for microscope images using the analysis on the four neighborhood gray level correlation has been presented

which is based on the study of the focusing principles and imaging processing of the microscope with the astigmatism considered as an ill factor to the focusing results. Method: firstly

to compute the four neighborhood gray level correlation of each pixel in every image sampled in the focusing processing. Then

to impair the influence of the astigmatism

some remedy measures such as weighted the correlation value by distances between the pixel and image center should be done in computing the focusing evaluation function

which is a quadratic polynomial about the average of the pixel neighborhood correlation. At last

analysis the variations of the function value of the sequential images

the focusing image corresponding the maximum function value. Result: the experiment results indicate that compared with the classical method

our function achieves the focusing sensitivity factor 0.3185~0.3268 higher

and improve the focusing correct rate with 0~40% under noise conditions. Conclusion: Our auto-focusing evaluation function can accurately estimate the focusing extents

and achieve high sensitivity and strong noise immunity.