How does sensor size impact depth of field and diffraction for macro photography?

Question

Macro photographers often stop down to very small apertures to maximize the razor thin depth of field when operating at such close focus distances. Smaller sensors have greater depth of field than larger sensors at the same f-stop with similar framing and subject distance, but smaller sensors have higher pixel pitch for a given pixel count and are thus impacted by diffraction sooner when stopping down.

Assuming a macro photographer wanted to fill the frame with a 36mm insect and enlarge the result to the same final size, which setup would have a greater depth of field in the final image if each picture was taken at the diffraction limited aperture: Nikon D4 (16MP) with a Tamron 90mm f/2.8 macro lens, or an Olympus OM-D E-M5 with a Panasonic 45mm f/2.8 macro lens?

Answer 1

Before we address the question directly, let's talk about the meaning of the Diffraction Limited Aperture.

Diffraction Limited Aperture (DLA) is only applicable at 100% viewing size. This is because DLA assumes a Circle of Confusion (CoC) equal to the pixel pitch of a particular sensor. The effects of diffraction at the DLA are only observable if the resulting image is magnified enough that the viewer can discretely resolve individual pixels. For an 18MP image viewed on a 23" HD (1920x1080) monitor that is the equivalent magnification of a 54"x36" print!

Take for example the 20.2MP full frame Canon 6D and compare it to the 20.2MP APS-C 70D. (I have easier access to the data for Canon gear). Both have the same resolution: 5472x3648.

• The 6D has a pixel pitch of 6.54µm and DLA of f/10.5
• The 70D has a pixel pitch of 4.1µm and DLA of f/6.6

Lets assume a 100mm lens on the 70D and a 160mm lens on the 6D. But then it gets a little tricky, because for a 36mm insect to fill the frame on the 6D (which has a 36x24 mm sensor) you need a 1:1 Maximum Magnification (MM). For the same 36mm insect to fill the frame of the 70D, you would only need an MM of 1:1.6 because the sensor of the 70D is only 22.5mm wide.

At 160mm a 1:1 MM is achieved at a focus distance of 16.8" (MFD interpolated from the specs for the Canon 180mm Macro lens). At 100mm a 1:1 MM is achieved at a distance of 12", so a 1:1.6 magnification would allow a distance of 19.2"

At the 6D's DLA of f/10.5 (the closet Av on the DoF chart I am using is f/11) using a 160mm lens focused at 16.8", the depth of field is 0.12 inches for an 8X10" print viewed at 10 inches.

At the 70D's DLA of f/6.6 (the closest Av on the DoF chart I am using is f/6.7) using a 100mm lens focused at 19.2", the depth of field is 0.19 inches for an 8X10" print viewed at 10 inches.

So strictly in terms of diffraction versus depth of field, the shorter lens with the smaller sensor would allow a greater DoF at the DLA for each camera.

This does, however, ignore the effects of noise and noise reduction on the detail present in the final image. The 1.5 stop narrower aperture used by the 6D is less than the 1.8 stop light gathering advantage of the larger sensor (1.6*1.6=2.56 2.56/√2=1.8). But the differences in sensor technology between two cameras from different manufacturers and generations of sensor evolution may well be greater than the very slight advantage here.

It also fails to take into account the differences in the actual shape of the aperture blades of various lenses and their effect on diffraction as well as variables in terms of acutance and other optical qualities between the two different lenses. These may well influence final image quality to a far greater degree than using an aperture beyond the DLA to get the same DoF.

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Since you've now modified your question with specific camera/lens combinations we will examine that comparison as well. Some data has been interpolated because we could not find exact specifications published.

• The Nikon D4 has a pixel pitch of 7.2µm and a DLA of f/11.5
• The Olympus OM-D E-M5 has a pixel pitch of 3.7µm and a DLA of f/5.9
• The Tamron SP AF 90mm f/2.8 Di Macro has a 1:1 MM at an MFD of 11.4"
• The Panasonic Leica DG Macro-Elmarit 45mm F2.8 has a 1:1 MM at an MFD of 6"

Due to the 2:1 difference in sensor sizes (linear), the Panasonic lens on the E-M5 would yield a 1:2 magnification at 12"

At the D4's DLA of f/11.5 (f/11 on the chart) using a 90mm lens focused at 11.4", the DoF is 0.19 inches.

At the E-M5's DLA of f/5.9 (f/5.6 on the chart) using a 45mm lens focused at 12", the DoF is 0.26 inches

Again, the (roughly) 2 stop difference in aperture is offset by the (roughly) 2 stop light gathering advantage of the D4 sensor. Note also that since your 36mm bug is occupying the long dimension of the sensor, the 4992 pixel width of the D4 is 7.5% higher resolution than the 4640 pixel width of the E-M5. (The D4 uses a 3:2 aspect ratio, the E-M5 uses a 4:3 aspect ratio)

Answer 2

In general shooting, provided you keep angle of view, camera position and size of entrance pupil the same, depth of field and diffraction will be the same regardless of sensor size!

The entrance pupil is the focal length divided by the f-number you are shooting at, e.g. a 45mm f/2.8 at f/2.8 has an entrance pupil that is 45/2.8 = 16mm. It's the size the aperture stop appears to be when viewed through the front element.

So with the equipment you list, a 90mm lens is required to give the same field of view when using the full frame D4. So to get the same 16mm entrance pupil you need to use 90/16 = 5.6, f/5.6 provided you set the camera to f/5.6 you will get the same depth of field.

What about diffraction?

The absolute size of the airy disc (the blurred area created from a sharp point of light as it passes through a small aperture) increases linearly with a larger f-number, so f/5.6 on the D4 causes a blur that is twice the radius of the EM5 (whose lens is at f/2.8) however because the sensor on the D4 is twice the height (and width) the blur has exactly the same overall effect on the image.

It's always worthwhile to think about blur and sharpness etc. in proportion to the image size. When thinking about diffraction most people immediately start trying to work out airy discs and pixel pitch and get confused when the number of pixels is different between different formats. Instead just think about blur in terms of the percentage of image and such issues go away!

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The key word in the first sentence is "in general shooting". Unfortunately when you get into the macro territory things get complicated, fast.

Firstly the focal length and aperture values stated for a lens are only valid with the lens focused at infinity. Most macro lenses focus closer by reducing focal length.

The aperture also behaves differently at high magnifications with the "effective" aperture taking over.

Finally the symmetry (difference in size between entry and exit pupils) of the lens plays a part, so without knowing what's inside the lens you can't be certain of the depth of field values.

If you're really concerned about depth of field and macro then you should be thinking about stacking shots rather than different camera bodies. A different sensor might give a small advantage but stacking gives a huge advantage.

Answer 3

I'm fairly certain you can't solve for it without additional variables. Resolution, pixel pitch, viewing distance, subject distance, focal length, subject depth all have impacts on how things balance out and don't seem to be in any simple linear way.

The amount of benefit you get from the focal length difference depends on how far the object is from the lens, how long it is and what the focal lengths needed are.

The amount of benefit from increasing the diffraction limit depends on the pixel pitch and the resolution of the camera (which also determines sensor size).

Finally, the viewing distance determines the cone of confusion (as long as there is enough resolution that it is limited by eyesight) and reduces the impact of both the diffraction limit and depth of field on apparent sharpness.