It is well-known that a lens of a given focal length will deliver different angles of view when used with cameras having different sized sensors. For example, the above image was made with a Nikon D90 and a Nikkor 200-500mm f/5.6E telephoto zoom lens at 500mm. The D90 is a DX format camera having a 1.5x crop factor. In other words, the DX sensor crops the outer portion of the image formed by the lens. As a result, photographs made with this camera will display an angle of view equivalent to that produced by a lens with 1.5x the actual focal length used. In the above image, the 200-500 is at 500mm but the angle of view matches that produced by a 750mm lens.
It is often said that a crop sensor camera will also produce an image having a greater depth of field. In other words, the same lens at the same focal length will produce, not just a wider angle of view when paired with a full frame camera, but also a shallower depth of field. The claim is that the DX sensor not only crops the angle of view but forces a significant increase in depth of field. That assertion is just plain wrong.
In the below test images, you’ll see side-by-side comparisons of photos made with Nikon FX (full frame) and DX (crop sensor) camera bodies. The cameras used were the full frame Nikon D610 and the DX format Nikon D90. These cameras were used with the following lenses:
- Nikkor 200-500mm f/5.6E VR
- Tamrom 70-200mm f/2.8 Di VC USD
- Tamron 24-70mm f/2.8 Di VC USD
To isolate sensor size as the only variable, the comparison images were made with the lenses at the same focal length, focal ratio and at the same distance from a fixed position subject. The Nikkor 200-500mm f/5.6E and Tamron 70-200mm f/2.8 Di VC USD were mounted on a tripod in a fixed position. The Tamron 24-70mm f/2.8 Di VC USD has no tripod collar or foot. The cameras were mounted to the tripod with the tripod in the same position for each set of exposures.
To create a large enough set of images to suitably address the question, each lens was used at a multiple focal lengths:
- Nikkor 200-500mm f/5.6E VR: 200mm, 300mm, 400mm and 500mm
- Tamrom 70-200 f/2.8 Di VC USD: 70mm, 100mm, 135mm and 200mm
- Tamron 24-70 f/2.8 Di VC USD: 50mm and 70mm
Each lens was used wide open at its smallest f-stop number. ISO and shutter speed were kept constant for exposures made at the same focal length with both cameras.
Why did I decide to test the notion that sensor size has a significant impact on depth of field? I performed this experiment to test my belief that that lens aperture and distance to subject are the two factors having the greatest impact on depth of field. In other words, if a lens is used at the same physical aperture and distance to make photographs of a fixed position subject with two cameras of different sensor size, the depth of field recorded in the two images should be identical or, at least, very nearly so.
If I’m correct in this belief, the images should confirm it. If I’m wrong and if crop factor needs to be applied to depth of field as well as to focal length, photos made under the above conditions should exhibit obviously different depths of field with the photo made using the full frame camera consistently displaying an obviously shallower depth of field than the photo made using the crop sensor body.
Keeping all this in mind, let’s go to the photos. Below, are ten composite images. The photo occupying the left half of each composite was made using the Nikon D610. The photo to the right of the divider was made using the Nikon D90. Since the same lens at the same focal length, f-stop and distance to subject was used to make each image in a composite, the image made with the crop sensor D90 (on the right) shows a narrower angle of view. In each composite, I’ve indicated similar sections of the two photos that, when compared, reveal both photos to have identical – or nearly so – depths of field. This conclusion is reached by comparing the relative size of the subject, a hula dancer toy, and the out of focus highlights and details in the background.
Comparison #1: Nikkor 200-500mm f/5.6E (200mm, f/5.6)
Comparison #2: Nikkor 200-500mm f/5.6E (300mm, f/5.6)
Comparison #3: Nikkor 200-500mm f/5.6E (400mm, f/5.6)
Comparison #4: Nikkor 200-500mm f/5.6E (500mm, f/5.6)
Comparison #5: Tamron 70-200 f/2.8 VC (70mm, f/2.8)
Comparison #6: Tamron 70-200mm f/2.8 VC (100mm, f/2.8)
Comparison #7: Tamron 70-200mm f/2.8 VC (135mm, f/2.8)
Comparison #8: Tamron 70-200mm f/2.8 VC (200mm, f/2.8)
Comparison #9: Tamron 24-70mm f/2.8 VC (50mm, f/2.8)
Comparison #10: Tamron 24-70mm f/2.8 VC (70mm, f/2.8)
Comparing the above ten photo sets, it’s clear the photographs capture equivalent depths of field despite the fact that they’re made with full frame and crop sensor cameras. As expected, the crop sensor camera captures a more narrow angle of view. However, a comparison of the relative size of the hula dancer toy with the details of the out of focus background reveals that the DX format Nikon D90 captures the same depth of field as the FX format Nikon D610. This flies in the face of the common (but mistaken) belief that crop sensors significantly alter depth of field.
To understand the performance of each camera as illustrated in the above photos, one need only understand that photographic depth of field is largely determined by two factors: distance to subject and lens aperture. Each lens was kept at a constant position and distance from the subject for the photos made with the two camera bodies. By keeping focal length and f-stop constant in each photographic set, lens aperture was kept constant.
The f-stop number describes the ratio of lens focal length to aperture. In other words, a 200mm, f/5.6 lens has an aperture of about 36mm. This is true regardless of the size of the sensor in the camera to which the lens is attached. Here’s a listing of the focal lengths and apertures for each set of photos:
Nikkor 200-500mm f/5.6E VR
- 36mm aperture (200mm, f/5.6)
- 54mm aperture (300mm, f/5.6)
- 71mm aperture (400mm, f/5.6)
- 89mm aperture (500mm, f/5.6)
Tamron 70-200mm f/2.8 VC
- 25mm aperture ( 70mm, f/2.8)
- 36mm aperture (100mm, f/2.8)
- 48mm aperture (135mm, f/2.8)
- 71mm aperture (200mm, f/2.8)
Tamron 24-70mm f/2.8 VC
- 18mm aperture (50mm, f/2.8)
- 25mm aperture (70mm, f/2.8)
As you review the above list, notice the constant f-stop results in increasing lens aperture as focal length increases. By keeping subject distance constant and increasing the physical aperture of the lens, depth of field becomes more shallow. By definition, the reverse is also true. With subject distance kept constant, decreasing lens aperture would result in a deeper or increased depth of field. And as illustrated by the above comparisons, keeping both subject distance and lens aperture constant produces constant depth of field. This holds true regardless of sensor size.
How is it, then, that so many photographers have come to accept the false assertion that crop sensor cameras make images having increased depth of field? The key to understanding this is the concept of equivalence. In simplest terms, equivalence describes two images made with different cameras and lens settings but having identical qualities. There are many factors that go into describing truly equivalent images. For the purposes of this discussion, we’ll focus on angle of the view and depth of field.
Let’s consider the above image set made with the Tamron 70-200mm f/2.8 VC. Due to its smaller sensor, a photograph made with the D90 captures a more narrow angle of view in comparison with an image made with the D610 at the same focal length. To capture an equivalent angle of view at the same distance from the subject, the D610 needs to use a greater focal length. At that increased focal length, the FX format camera will capture an angle of view equivalent to that recorded by the D90.
If both lenses are used at the same f-stop of f/2.8, their respective apertures will be about 46mm for the 130mm, f/2.8 lens on the D90 and 71mm for the 200mm, f/2.8 lens on the D610. Bear in mind, both cameras are at the same distance from the subject. Due to the larger physical aperture of the 200mm focal length lens, it records a shallower depth of field. To match the depth of field of the D90, the D610 is closed down from f/2.8 to f/4. This closes the aperture from 71mm to 50mm, which roughly matches the depth of field recorded by the D90 and its 46mm aperture.
Also, compare the quality of the out of focus background detail in the photos made with the DX format D90 (left most column) with the same detail in the second set of photos made with the FX format D610 (middle of three columns). Pay particular attention to the grouping of four bokeh balls to the left of the lunar lander model. In the D90 photos and in the equivalent D610 photos (right most column), that grouping is well defined with clear separation. In the middle column of D610 photos, that grouping is more diffuse, less well defined and not as clearly separated from the background.
This is what we would expect, considering that all the photos in that collection were made with the cameras and lenses at the same distance from the subject. The first and third column sets of images made with the D610 were made with the same lens aperture as the D90. The third column set of D610 images were made at an equivalent focal length to the D90 images. Both the angle of view and depth of field are equivalent. The first set (left column) of D610 images, while showing a wider angle of view, have equivalent depth of field as the D90 images. Again, this is exactly what one would expect given that the D90, and first and third set of D610 images were made at the same aperture, while the second set (middle column) of D610 photos were made at a larger aperture.
Another approach to producing equivalent depths of field, would have been to increase the lens aperture on the D90. The D90 would need a 130mm f/1.8 lens, which would have a 72mm aperture. That’s very nearly identical to the 71mm aperture of the 200mm, f/2.8 lens on the D610.
If equivalence is your objective, applying the crop factor to the f-stop allows you to calculate the aperture needed to make a photograph having an equivalent depth of field at a focal length delivering an equivalent angle of view. This adjustment can go either way. We can use a larger f-stop (multiply by the crop factor) to close down the aperture of the lens on the larger sensor camera or we can use a smaller f-stop (divide by the crop factor) to open the aperture of the lens on the smaller sensor camera. Either approach will produce equivalent apertures on the two cameras, which allows them to capture matching depths of field.
This is what has led so many photographers to mistakenly conclude that crop sensors significantly alter depth of field. What folks overlook is that the crop factor is applied to allow the lenses on the cameras to operate at the same physical aperture. Again, the key to understanding depth of field is recognizing that distance to subject and lens aperture are the critical factors. If you keep subject distance constant, keeping lens aperture constant will deliver equivalent depth of field. This holds true even if the lenses are used at focal length delivering non-equivalent angles of view.
Wildlife photographers often choose to shoot with crop sensor cameras to effectively bring the animals closer. They want the narrower angle of view delivered by the crop sensor. Shooting at 500mm f/4 with a DX camera will not only produce a larger image of the subject (in comparison with a photograph made using the same lens at the same distance on an FX camera), the DX camera will also record the same shallow depth of field and beautiful, buttery bokeh. That’s a huge advantage and a big reason why crop sensor cameras are so popular with sports and wildlife photographers. Of course, the smaller sensor also captures less total light with each exposure and this has implications for image noise. But that’s another blog entry.
In the meantime, armed with this new information and understanding of the role lens aperture plays in depth of field, let’s get out and shoot.
Bill Ferris | March 2016