Surface irregularity errors are conventionally used to specify fabrication accuracy of spherical, aspheric, or plane surfaces. However, in some cases, the amplitude of the irregularities fails to fully describe the surface accuracy requirement when the pupil size is small compared to the surface diameter. In such cases, the irregularity slope will induce distortion. A spatially dependent representation of the irregularity slope is proposed and implemented to specify the surface accuracy. As an optical design example, we study in detail the case of the front surfaces of a fish-eye lens and a panomorph lens. Panoramic lenses are characterized by a small entrance pupil and by important distortion. For both lenses, we found that the novel field-dependent mathematical descriptor provided a nearly perfect agreement with Monte Carlo analyses and can be used to specify the spatially dependent irregularity requirement. The approach is not limited to wide-angle lenses.
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