When you have a square aperture the NA is different in different directions. This corresponds to the beamwidth, or resolution of a square antenna.

A square aperture has a bigger NA across the diagonals than across the axes aligned with the sides. The diffraction limited focal spot will not be round, but diamond shaped.

My opinion is that the term NA is appropriate for rotationally symmetric systems only. Or it is just a measure of the angle taking into account the index.

What is the purpose of the question ?

The term NA might be appropriate only for rotationally symmetric systems, but the formula is applicable for other shapes and is the same one that gives the width of pixels (resolution) of synthetic aperture radars, for instance.

Agree. Then the question was that of the resolution of a system with square aperture. It is obvious what kind of physics we need but not necessarily a question of how the term NA is defined.

Henning Rehn

I've been working on the partial coherence analysis of a maskless lithography tool based on DMD, which contains the Kohler integrator for the illumination system.

In the field of lithography with mask,DUV tool, for example, the partial coherence can be defined as sigma=NA(illumination)/NA(objective).I take it that this formula can be used in the maskless litho field, so I need to know the NA(illumination). There are several illumination modes except the square shaped one, as you can see below

Hi Steven, my recommendation is to go one step back and ask for the origin of your sigma formula. Consider this like pupil fill.

Hi Henning,

The pupil fill ratio is the fundamental method. Thanks.

Ronian Siew

Hi Ronian,

Thanks for the detailed explanation.

Henning Rehn

Hi Henning,

I've been evaluating an illumination design for the self-made MTF measurement system recently. It's a 3-element design,as you can see, the difference between the illuminance and the luminous intensity on the receiver is big. The illuminance distribution is uniform , while the luminous intensity distribution is kind of bat-wing. Is this kind of design supposed to have the difference between the illuminance and the luminous intensity or did I have the wrong setting in this model?

Hi Steven, there's nothing wrong. You are imaging the source and thus get a homogeneous irradiance pattern. If you need homogeneous intensity, you need to check that aspect of the imaging. You can set up your lens system in an afocal way and will see some aberrations.

Henning Rehn

Thanks for your instant reply, Henning. I'll check the design thoroughly.