Influence of contrast on the recognition of defocused letters: a geometrical model

We show how contrast (C) affects the recognition of defocused letters. To do this, the maximum distance (threshold distance) at which a subject, with an induced refraction of -5.5 D, can recognize a letter was determined. Our results show that when C = 1, the recognition threshold distance is such that the ratio eta/xi, between the pseudoimage of the letter (eta) and the blur circle (xi), corresponding to any point of the letter at this distance is about eta/xi = 2; the exact value depends on the difficulty of recognition, in agreement with previous experiments. This ratio represents the sharpness of the image in a geometrical treatment of image formation, providing a geometrical criterion for recognition. Reduction in contrast can be compensated by improving the geometrical sharpness; i.e. bringing the object closer to the subject's are point. Our results show that the increment of eta/xi as a function of the contrast is between C = 0.1 and 1.0. We suggest that a similar geometrical criterion for recognition could be used for any contrast (at least down to C = 0.1 and defocus > 1 D), provided that the proper value of eta/xi is used in each case. On this basis we propose a purely geometrical model, which agrees well with the data and predicts the relationships between tolerance to defocus, contrast and visual acuity; including the well-known relation between visual acuity and defocus when contrast is unity.