Skip to main content
U.S. flag

An official website of the United States government

Official websites use .gov
A .gov website belongs to an official government organization in the United States.

Secure .gov websites use HTTPS
A lock ( ) or https:// means you’ve safely connected to the .gov website. Share sensitive information only on official, secure websites.

On the Diffraction Limit for Lensless Imaging



Klaus Mielenz


The diffraction limit for lensless imaging, defined as the smallest obtainable point image, is analyzed and compared to the corresponding limit for imaging with lenses by means of theoretical considerations and numerical computations using the Fresnel-Lommel diffraction theory for circular apertures. The numerical result obtained for the best configuration parameter u which defines the optical setup is the same (u = ) as the value reported in a classical paper by Petzval and is consistent with the quarter-wave resolution criterion, but smaller than a value (u = 1.8 ) found by Lord Rayleigh which is shown to be consistent with the Sparrow criterion of resolution. The numerical values of other measures of image size are reported and compared to equivalent parameters of the Fraunhofer-Airy profile which governs imaging with lenses.
Journal of Research (NIST JRES) -
104 No. 5


aperture diameter, Fraunhofer-Airy profile, Fresnel-Lommel theroy, image size irradiance, lensless imaging, Petzval, radiant flux, Rayleigh, resolution


Mielenz, K. (1999), On the Diffraction Limit for Lensless Imaging, Journal of Research (NIST JRES), National Institute of Standards and Technology, Gaithersburg, MD (Accessed July 13, 2024)


If you have any questions about this publication or are having problems accessing it, please contact

Created November 17, 1999, Updated February 17, 2017