Diffraction-Limited Lenses and the Sharpest Possible Photo

There are actually physical limits on how sharp your photos can be. Physics itself demands these limits, no matter how much you’re willing to spend on a premium lens. Your camera sensor places additional limits on just how sharp a photograph can be.

Lens Limits

Something called the “Airy Disc”, named after George Airy (1801-1892), places absolute limits on a lens’ sharpness. A lens can only focus a point of light within certain bounds, related to the color of the light being focused.

Airy disc in 3 dimensions, courtesy Google AI

Light is actually a 3-D thing. A point of light focused onto a camera sensor looks more like a splash of water. Light waves of different colors have different lengths, where blue light is shorter than red light. Green light is somewhere in the middle.

When a lens aperture is stopped down, the size of this Airy disc starts growing in diameter. The Airy disc diameter is only a function of the aperture f-number and the color (frequency) of light. When apertures are idealized as being a perfect circle, the Airy disc diameter, measured in microns, can be estimated to be 1.34 times the aperture f-number for green light (549nm or 0.549um). For blue light, for instance, the Airy disc diameter is smaller. Green light can be between 500nm and 600nm, but 549 was chosen here.

The Airy disc formula is:

Airy_disc_dia = (2.44 X frequency_um X F_stop)

For the above,

  frequency_um = 0.549

Airy disc sizes with green light

In the table above, I’ve shown how big the Airy disc gets at different lens apertures. I also mention a camera sensor with pixels that are 4.35 microns across, such as my Nikon Z9 and Z8.

This shows that a lens that has absolutely perfect optics can only focus a point of light within limits, depending upon the lens aperture and the light color (frequency).

Camera Sensor Limits

For you to notice the image getting fuzzy, the size of this Airy disc has to grow until it covers more than a single pixel on your camera sensor. A rule of thumb is to start getting concerned about diffraction when the Airy disc grows to be two pixels across or more. For making prints, this rule can be loosened up considerably.

For camera sensors that have anti-alias filters (to help rid any Moire effects) the images are even fuzzier.

The sharpness limits for the camera sensor are summarized by what’s called the Nyquist Limit and the Kell Factor.

According to Edmund Optics, the absolute limiting resolution of a sensor is the Nyquist Limit which is half of the sampling frequency (pixels/mm). For the Nikon Z9/Z8, the sensor is 8280 X 5520 pixels. The dimensions are 35.9mm X 23.9mm. The Nyquist limit is (8280/35.9)/2 pixels per millimeter (231/2 pix/mm) horizontal or (5520/23.9)/2 pixels/mm vertical, or again (231/2) pix/mm.

 The Nyquist limit of (231/2) lp/mm is then 115.5 lp/mm. 

The typical actual frequency response includes what’s called the “Kell Factor” named after Raymond Kell, which is conservatively set to 0.7.  This value helps compensate for the physical space between the light-sensitive portions of the pixels, and to avoid patterns similar to the moire effect. This means the practical actual sensor frequency response limit is now (115.5 X 0.7) or 80.85 lp/mm.

Given this information, any measured lens resolution above 80.85 lp/mm for this camera sensor is unreliable.

My Best Lens

For me personally, my best lens is the Nikkor 500mm f/5.6 PF. I tested it on my Nikon Z8 camera, where I found that I needed to do minor focus fine-tuning to optimize its focus.

Several focus test results for my 500mm f/5.6 PF lens

The resolution results from the data plotted above got an average MTF50 resolution of 77.1. The peak reading was 84.1, with a standard deviation of 5.3.

Using the MTF50 average of 77.1 lp/mm, this lens is quite near the calculated sensor limit of 80.85 lp/mm. As an aside, these measurements are better than I have been able to obtain using my Nikon Z9, although I haven’t been able to figure out why that is (even with focus fine-tune).

If Nikon had made this lens any sharper, you’d never be able to detect it without buying a camera with smaller pixels in the sensor.

The absolute sharpest possible lenses would also have the widest aperture, and not suprisingly they'd be super heavy with all of that glass.