Tag Archives: angle of view

Sensor Size and Depth of Field

It is commonly said that crop sensor cameras make images having both a narrower field of view and a greater depth of field. Well, that's partly right. (Bill Ferris)

It is commonly said that crop sensor cameras make images having both a narrower field of view and a greater depth of field. Well, that’s partly right. (Bill Ferris)

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)

The photo to the left of the divider was made with the Nikon D610 and Nikkor 200-500mm f/5.6E at 200mm, f/5.6, ISO 400, 1/200-second. The photo on the right was made with the same lens at the same distance from subject also at 200mm, f/5.6, ISO 400, 1/200-second. (Bill Ferris)

The photo to the left of the divider was made with the Nikon D610 and Nikkor 200-500mm f/5.6E at 200mm, f/5.6, ISO 400, 1/200-second. The photo on the right was made with the Nikon D90, the same lens at the same distance from subject also at 200mm, f/5.6, ISO 400, 1/200-second. (Bill Ferris)

Comparison #2: Nikkor 200-500mm f/5.6E (300mm, f/5.6)

The photo to the left of the divider was made with the Nikon D610 and Nikkor 200-500mm f/5.6E at 300mm, f/5.6, ISO 400, 1/200-second. The photo on the right was made with the same lens at the same distance from subject also at 300mm, f/5.6, ISO 400, 1/200-second. (Bill Ferris)

The photo to the left of the divider was made with the Nikon D610 and Nikkor 200-500mm f/5.6E at 300mm, f/5.6, ISO 400, 1/200-second. The photo on the right was made with the Nikon D90, the same lens at the same distance from subject also at 300mm, f/5.6, ISO 400, 1/200-second. (Bill Ferris)

Comparison #3: Nikkor 200-500mm f/5.6E (400mm, f/5.6)

The photo to the left of the divider was made with the Nikon D610 and Nikkor 200-500mm f/5.6E at 400mm, f/5.6, ISO 400, 1/250-second. The photo on the right was made with the same lens at the same distance from subject also at 400mm, f/5.6, ISO 400, 1/250-second. (Bill Ferris)

The photo to the left of the divider was made with the Nikon D610 and Nikkor 200-500mm f/5.6E at 400mm, f/5.6, ISO 400, 1/250-second. The photo on the right was made with the Nikon D90, the same lens at the same distance from subject also at 400mm, f/5.6, ISO 400, 1/250-second. (Bill Ferris)

Comparison #4: Nikkor 200-500mm f/5.6E (500mm, f/5.6)

The photo to the left of the divider was made with the Nikon D610 and Nikkor 200-500mm f/5.6E at 500mm, f/5.6, ISO 400, 1/250-second. The photo on the right was made with the same lens at the same distance from subject also at 500mm, f/5.6, ISO 400, 1/250-second. (Bill Ferris)

The photo to the left of the divider was made with the Nikon D610 and Nikkor 200-500mm f/5.6E at 500mm, f/5.6, ISO 400, 1/250-second. The photo on the right was made with the Nikon D90, the same lens at the same distance from subject also at 500mm, f/5.6, ISO 400, 1/250-second. (Bill Ferris)

Comparison #5: Tamron 70-200 f/2.8 VC (70mm, f/2.8)

The photo to the left of the divider was made with the Nikon D610 and Tamron 70-200mm f/2.8 VC at 70mm, f/2.8, ISO 400, 1/400-second. The photo on the right was made with the same lens at the same distance from subject also at 70mm, f/2.8, ISO 400, 1/400-second. (Bill Ferris)

The photo to the left of the divider was made with the Nikon D610 and Tamron 70-200mm f/2.8 VC at 70mm, f/2.8, ISO 400, 1/400-second. The photo on the right was made with the Nikon D90, the same lens at the same distance from subject also at 70mm, f/2.8, ISO 400, 1/400-second. (Bill Ferris)

Comparison #6: Tamron 70-200mm f/2.8 VC (100mm, f/2.8)

The photo to the left of the divider was made with the Nikon D610 and Tamron 70-200mm f/2.8 VC at 100mm, f/2.8, ISO 400, 1/400-second. The photo on the right was made with the same lens at the same distance from subject also at 100mm, f/2.8, ISO 400, 1/400-second. (Bill Ferris)

The photo to the left of the divider was made with the Nikon D610 and Tamron 70-200mm f/2.8 VC at 100mm, f/2.8, ISO 400, 1/400-second. The photo on the right was made with the Nikon D90, the same lens at the same distance from subject also at 100mm, f/2.8, ISO 400, 1/400-second. (Bill Ferris)

Comparison #7: Tamron 70-200mm f/2.8 VC (135mm, f/2.8)

The photo to the left of the divider was made with the Nikon D610 and Tamron 70-200mm f/2.8 VC at 135mm, f/2.8, ISO 400, 1/400-second. The photo on the right was made with the same lens at the same distance from subject also at 135mm, f/2.8, ISO 400, 1/400-second. (Bill Ferris)

The photo to the left of the divider was made with the Nikon D610 and Tamron 70-200mm f/2.8 VC at 135mm, f/2.8, ISO 400, 1/400-second. The photo on the right was made with the Nikon D90, the same lens at the same distance from subject also at 135mm, f/2.8, ISO 400, 1/400-second. (Bill Ferris)

Comparison #8: Tamron 70-200mm f/2.8 VC (200mm, f/2.8)

The photo to the left of the divider was made with the Nikon D610 and Tamron 70-200mm f/2.8 VC at 200mm, f/2.8, ISO 400, 1/400-second. The photo on the right was made with the same lens at the same distance from subject also at 200mm, f/2.8, ISO 400, 1/400-second. (Bill Ferris)

The photo to the left of the divider was made with the Nikon D610 and Tamron 70-200mm f/2.8 VC at 200mm, f/2.8, ISO 400, 1/400-second. The photo on the right was made with the Nikon D90, the same lens at the same distance from subject also at 200mm, f/2.8, ISO 400, 1/400-second. (Bill Ferris)

Comparison #9: Tamron 24-70mm f/2.8 VC (50mm, f/2.8)

The photo to the left of the divider was made with the Nikon D610 and Tamron 24-70mm f/2.8 VC at 50mm, f/2.8, ISO 400, 1/640-second. The photo on the right was made with the same lens at the same distance from subject also at 50mm, f/2.8, ISO 400, 1/640-second. (Bill Ferris)

The photo to the left of the divider was made with the Nikon D610 and Tamron 24-70mm f/2.8 VC at 50mm, f/2.8, ISO 400, 1/640-second. The photo on the right was made with the Nikon D90, the same lens at the same distance from subject also at 50mm, f/2.8, ISO 400, 1/640-second. (Bill Ferris)

Comparison #10: Tamron 24-70mm f/2.8 VC (70mm, f/2.8)

The photo to the left of the divider was made with the Nikon D610 and Tamron 24-70mm f/2.8 VC at 70mm, f/2.8, ISO 400, 1/640-second. The photo on the right was made with the same lens at the same distance from subject also at 70mm, f/2.8, ISO 400, 1/640-second. (Bill Ferris)

The photo to the left of the divider was made with the Nikon D610 and Tamron 24-70mm f/2.8 VC at 70mm, f/2.8, ISO 400, 1/640-second. The photo on the right was made with the Nikon D90, the same lens at the same distance from subject also at 70mm, f/2.8, ISO 400, 1/640-second. (Bill Ferris)

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.

This set of images compares performance between crop sensor and full frame DSLR bodies. The images in the left column were made with a Nikon D90. Images in the right three columns were made with a Nikon D610. Both cameras used the same Tamron 70-200mm f/2.8 Di VC USD zoom lens, which was set up on a tripod to ensure it would not change position during the test. Both cameras used ISO 200, center point average metering and were operated in Aperture Priority. The subject in these photos is a scale model of the Lunar Excursion Module (LEM) from the Apollo program.

This set of images compares performance between crop sensor and full frame DSLR bodies. The images in the left column were made with a Nikon D90. Images in the right three columns were made with a Nikon D610. Both cameras used the same Tamron 70-200mm f/2.8 Di VC USD zoom lens, which was set up on a tripod to ensure it would not change position during the test. (Bill Ferris)

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

What the f/#?

The Tamron 70-200 f/2.8 Di VC USD zoom lens has a focal ratio of f/2.8. This defines the largest aperture the lens is capable of having at all focal lengths throughout the zoom range. Operating at f/2.8, the focal length selected will be 2.8X the size of the aperture. While the focal length range is 70-200mm, the range of largest apertures is 25mm at a 70mm focal length to 71mm at 200mm focal length.

The Tamron 70-200 f/2.8 Di VC USD zoom lens has a constant focal ratio of f/2.8. This defines the largest aperture the lens will have throughout the zoom range. Operating at f/2.8, the focal length selected will be 2.8X the aperture. With a focal length range of 70-200mm, the widest aperture varies from 25mm at a focal length of 70mm to 71mm at a 200mm focal length. (Bill Ferris)

Let’s nerd out with some tech talk. Let’s chat about focal ratio.

Focal ratio is a rarely seen or heard phrase in online photography blogs and forums, which is surprising when you consider the important role focal ratio plays in photography. Focal ratio describes the size of a lens’s focal length relative to its aperture. It is typically expressed as an f-number, such as f/2.8. Ironically, when photographers start talking about lens aperture, it’s more than likely they’re actually discussing focal ratio. Let’s see if we can sort all this out.

We’ll begin at the beginning. Focal length is typically the first number mentioned when describing a lens. A 50mm lens has a focal length of, wait for it…50mm or roughly two inches. One may be inclined to think focal length is the distance from the front of the lens to the back, but it’s not. Focal length is the distance from the optical center of the lens to the image plane (film or sensor) where the image is formed. The optical center is usually inside the lens and is sometimes referred to as the point of convergence; the point where two light rays converge and cross.

The above diagram shows a cross section of the Nikkor 50mm f/1.4 lens. The focal length of the lens is 50mm, which is measured from the optical center of the lens to the image plane at the sensor.

The above diagram shows a cross section of the Nikkor 50mm f/1.4 lens. The focal length of the lens is 50mm, which is measured from the optical center of the lens to the image plane at the sensor.

Focal length determines how much the image is magnified. This is typically described as the angle of view produced by the lens. A 50mm lens produces a 47° (on a diagonal) angle of view at the image plane of a 35mm camera body. A 24mm lens delivers an 84° angle of view and a 200mm lens presents a 12° angle of view. Since the angle of view produced by a 50mm lens is similar to that of normal vision, it is known in 35mm photography as a normal lens. 24mm is a wide angle focal length and a 200mm is a telephoto lens.

Of course, 35mm is just one of many photographic formats. A photographic format is defined by the physical size of the medium used to record the image. In film photography, 35mm describes the length of the long side of a slide or film negative. Today’s digital cameras use light-sensitive CMOS sensors to record images. In full frame digital cameras, the sensor measures 36mm on the longest side. APS-C digital cameras have sensors that are about 23mm on the longest side. The camera in your smartphone or tablet is probably built around a sensor no larger than about 10 millimeters. What does sensor size have to do with this topic? A lot.

The above diagram illustrates the relative sizes of common digital camera sensor formats. The largest shown is a full frame (FX) sensor. The smallesst (lower left corner) is representaive of a typical smart phone (1/2.3") sensor.

The above diagram illustrates the relative sizes of common digital camera sensor formats. The largest shown is a full frame (35mm equivalent) sensor. The smallest (lower left corner) is representative of a smartphone (1/2.3″) sensor.

The smaller the sensor or film medium, the farther you need to be from your subject to match the field of view delivered by a given focal length lens. Imagine standing 10 feet from your subject with a full-frame DSLR camera and framing your subject head-to-toe using a normal 50mm lens. If you were to mount the same lens on an APS-C camera body, that camera’s smaller sensor would cut off or crop a portion of the image produced by the lens. You would need to step back to a distance of about 15 feet to reproduce the angle of view you had with the full frame camera body.

Another factor to consider when shooting with a “crop sensor” body is the effect of sensor size on depth of field. Depth of field (DOF) is the range of distances – nearest to farthest – in an image that appear acceptably sharp and in-focus. DOF is determined by magnification (lens focal length) and by the lens focal ratio or f-number. In a nutshell, bringing the subject closer decreases depth of field. Moving the subject farther away increases depth of field. As depth of field increases, a deeper portion of the image appears in focus. As depth of field decreases, only a narrow or shallow range looks sharp and in focus.

Both photographs were made using a Nikon D610 with Tamron 70-200 Di VC USD zoom lens at 125mm. The image on the left was shot at f/2.8 and has a much shallower depth of field. The image on the right was shot at f/32 and presents a much wider depth of field.

The above photographs were made using a Nikon D610 and Tamron 70-200mm f/2.8 Di VC USD zoom lens at 125mm. The image on the left was shot at f/2.8 and has a much shallower depth of field. The image on the right was shot at f/32 and shows much more of the field in focus.

As mentioned, focal ratio also has an effect on depth of field. For any given focal length, increasing focal ratio (making the f-number larger) increases depth of field while decreasing focal ratio (making the f-number smaller) reduces depth of field. We’ve already discussed the cropping effect of shooting with a smaller sensor. Stepping back to reproduce a desired angle of view increases depth of field. Zooming or changing lenses to shoot with a shorter focal length (to match the field of view provided by a full frame sensor body) increases depth of field.

One can compensate for the increased depth of field which results from the adjustments commonly made to expand the angle of view delivered by a crop sensor camera by shooting with smaller f-numbers. For example, shooting with a 35mm lens at f/1.4 will allow an APS-C sensor body to produce photographs having the same framing and depth of field as images made from the same position using a 50mm f/2.0 lens on a full frame body.

Let’s explore this in a bit more detail. Suppose you’re shooting with two cameras, one full frame and the other a crop sensor, and using the same 50mm lens with both. Its effective focal length (the focal length matching the angle of view delivered to the sensor) will be 50% longer or 75mm on the APS-C body. At f/4, the 50mm lens will have an aperture of 12.5mm. If we step back to compensate for the more narrow angle of view, the effective focal ratio (the focal ratio delivering an equivalent depth of field from the distance at which this lens matches the angle of view delivered to a full frame camera) will be f/6. Its effective 75mm focal length divided by the 12.5mm aperture equals six.

Do you see the relationship? We’re using an f/4 lens on an APS-C body. When the goal is to match the angle of view and depth of field produced by a full frame camera, we can determine the effective focal ratio at which a crop sensor camera needs to operate by dividing the focal ratio of the lens by the crop factor. The crop factor is 1.5 and the effective focal ratio (for depth of field) is f/6.

Here’s an illustration.

These images illustrate how to use a crop sensor camera to match both the angle of view and the depth of field delivered by a full frame body. I used a Nikon D610 and Nikon D90 to make photographs of the same toy caboose. Both cameras used a Tamron 70-200 f/2.8 Di VC USD lens. The lens was mounted on a tripod and the bodies switched out to ensure the lens would not move from its position during the test. The D610 uses a 36mm sensor and shot at 105mm, f/4 to make both images. The D90 uses an APS-C sensor with a 1.5X crop factor. I shot at 75mm, f/4 to make the first image. Comparing the first (top) images, we see that the D90 delivered a similar angle of view as the D610 but a comparison of the background shows the D610 to have a more shallow depth of field. The background in the D90 image is just skosh nearer to being in focus. For the second image, I applied the conversion factor and shot with the D90 at 70mm, f/2.8. A comparison of this image with the D610 image shows both to have delivered similar angles of view and similar depth of field. (Bill Ferris)

These images illustrate how to use a crop sensor camera to match both the angle of view and the depth of field delivered by a full frame body. I used a Nikon D610 and Nikon D90 to make photographs of the same toy caboose. Both cameras used the same Tamron 70-200 f/2.8 Di VC USD lens. The lens was mounted on a tripod and the bodies switched out to ensure the lens would not move from its position during the test. The D610 is built around a 36mm sensor and was used at 105mm, f/4 to make both images. The D90 has an APS-C sensor with a 1.5X crop factor. I shot at 70mm, f/4 to make the first image. Comparing the first (top) images, we see that the D90 delivered a similar angle of view as the D610 but a comparison of background detail reveals the D610 to have a more shallow depth of field. The background in the D90 image is just a skosh nearer to being in focus. For the second image, I applied the conversion factor and shot with the D90 at 70mm, f/2.8. A comparison of this image with the D610 image shows both to have delivered similar angles of view and similar depth of field. (Bill Ferris)

So, we’ve demonstrated that, in comparison with full frame cameras, crop sensor camera bodies produce images having narrower angles of view and, when adjustments are made to compensate for this, increased depth of field. We’ve also demonstrated that you can compensate for these performance factors. Either increase the distance between you and the subject or use a shorter focal length to increase the angle of view. Shoot at a smaller focal ratio (f-number) to make the depth of field more shallow. Next, we’ll explore the relationship between sensor size and length of exposure. Here’s a heads up, the outcome may not be what you expect.

I used my Nikon D610 (full frame) and Nikon D90 (APS-C) to take a series of exposures of a toy train engine. The toy steam engine was set up outside on a small tray table. The sky was overcast with nice, even lighting throughout the test. Both bodies used the same Tamron 70-200mm f/2.8 Di VC USD lens, which was set at 70mm. I selected ISO 200 on both cameras for all exposures. The zoom lens was set up on a tripod and the camera bodies were switched out without changing the position of the lens. I used each camera to make exposures at f/2.8, f/4, f/5.6, f/8, f/11, f/16, f/22 and f/32. I shot in aperture priority on both cameras and let their internal brains select the proper exposure.

Below, are pairs of images showing the photographs made at the same settings with the two bodies, side-by-side. All are unedited JPEGs. Keep in mind that the sensor in the D90 body cropped the image to match the angle of view produced by a 105mm lens.

In this comparison, photographs of the same subject made with a Nikon D610 (left) and a Nikon D90 (right) are shown, side-by-side. Both cameras shot at ISO 200. Both cameras used the same Tamron lens at 70mm. The lens was mounted on a tripod to ensure it would remain in the same position throughout the test. For each focal ratio, both cameras used the same exposure. (Bill Ferris)

In this comparison, photographs of the same subject made with Nikon D610 (left) and Nikon D90 (right) cameras are shown, side-by-side. Both cameras were set to ISO 200. Both cameras used the same Tamron lens at 70mm. The lens was mounted on a tripod to ensure it would remain in the same position throughout the test. At each focal ratio, both cameras metered the scene as having the same brightness and chose the same exposure. (Bill Ferris)

Let’s talk more about this f-number thing. You’ll recall that focal ratio describes the ratio of the focal length of the lens to the aperture of the lens. A 50mm lens at f/2.0 has a focal length that is 2-times its aperture. Therefore, the lens aperture at f/2.0 will be 25mm. At f/4.0, the aperture is 12.5mm; at f/8.0, 6.25mm and so on. The relationship between aperture and focal ratio is pretty straight forward: for any given focal length, decreasing aperture increases focal ratio and increasing aperture decreases focal ratio.

Rarely, however, do photographers talk about the f-number as a focal ratio. More commonly, they talk about it as a lens aperture. They talk about an f/2.0 lens having a larger aperture than an f/4.0 lens. It’s an accurate statement, if we’re talking about the same lens at different focal ratios. But this is just one of many scenarios where focal ratios are compared.

Let’s consider the scenario of discussing different lenses. Suppose we’re comparing a 50mm lens to a 100mm lens. Suppose the 50mm lens is being used at f/2 and the 100mm lens is set to f/4. One might think the 50mm lens, by virtue of having a smaller f-number, will have a larger aperture. In fact, both lenses have identical 25mm apertures. It simply isn’t the case that every f/1.4 lens has a larger aperture than every f/8 lens. In reality, it is quite common for a lens operating at a large f-number to have a larger aperture than a lens working at a small f-number. I would wager to guess that there isn’t a focal ratio at which a 600mm lens doesn’t have a larger aperture than the fastest focal ratio smartphone.

One quality that does translate across different lenses and cameras, is the speed of the imaging system. What does speed have to do with photography? To understand, it helps to think of a properly exposed photograph as one where a certain intensity of light needs to fall upon the sensor at the image plane. Think of light as water, the sensor as a container used to collect water (light) and the lens as the opening through which water is poured into the container.

That said – and this next point is critical – a properly exposed image is not determined by the total quantity of light delivered to the sensor. The length of a proper exposure is determined by the average brightness of the image falling on the sensor. To better understand this, we’re going to introduce a new concept: surface brightness.

The above illustrates the concept of Surface Brightness in photography. For a properly exposed image, the camera's optical system must collect and deliver light having a surface brightness (brightness or intensity per square millimeter) to the sensor. This is represented by the evenly deep layer of "blue" light collected bu the sensor. If you use the same lens on a crop sensor body, the same intensity of light (represented by the central red region) is delivered to the sensor. Being smaller, the crop sensor collects less total light. However, the surface brightness of the image (the brightness per square millimeter) is identical to that of the larger sensor. (Bill Ferris)

The above illustrates the concept of Surface Brightness in photography. For a properly exposed image, the camera’s optical system must collect and deliver light having a surface brightness (brightness per square millimeter) to the sensor. This is represented by the thick layer of “blue” light collected by the sensor. The thickness of the layer represents the intensity or average brightness of the image. If we use the same lens on a crop sensor body, the same intensity (thickness) of light is delivered to the sensor. This is represented by the central red zone on the sensor. Being smaller, the crop sensor collects less total light. However, the surface brightness of the image is identical to that of the larger sensor. (Bill Ferris)

Earlier, a correct exposure was described as one where a container (sensor) is filled to the correct depth (intensity) with water (light). It doesn’t matter if the container is large enough to hold one gallon or 100 gallons. As long as it’s filled to the proper depth, the exposure will be good. In this example, the depth of the water represents the average brightness of the image at the image plane. Another way to describe the average brightness or intensity of light, is to talk about image surface brightness.

Surface brightness is defined as a brightness per unit area. In photography, we can define surface brightness as the brightness of light per square millimeter falling on the film or sensor. It is not a total volume or quantity of light. Rather, it is an average intensity of light. Surface brightness is strictly determined by the focal ratio of the optical system. The lens f-number determines the length of the exposure needed to deliver light of a certain intensity to the sensor. A full frame camera, crop sensor camera and smartphone camera focused on the same subject – and all operating at f/2.0 – will deliver the same light intensity per square millimeter (the same surface brightness) to their respective sensors during the same length exposure.

The relative sizes of full frame (pink) and APS-C (blue) sensors is illustrated above. The effects of a crop frame sensor include an increase in effective focal length and an increase in effective depth of field.

The relative sizes of full frame (pink) and APS-C (blue) sensors is illustrated above. The effects of a crop frame sensor include an increase in effective focal length and effective depth of field.

Despite the fact that a crop sensor doesn’t collect as much total light during an exposure as a full frame sensor, the intensity or surface brightness of the images formed on both sensors will be the same. We saw this at work in the above illustrations comparing exposures made with the D610 and D90. Despite the fact that, during each set of exposures, the D90’s smaller sensor collected less total light than the full frame sensor of the D610, the image made by the D90 was still properly exposed. This is because the exposures made by both cameras produced images having identical surface brightness at the image plane.

This set of images compares performance between crop sensor and full frame DSLR bodies. The images in the left column were made with a Nikon D90. Images in the right three columns were made with a Nikon D610. Both cameras used the same Tamron 70-200mm f/2.8 Di VC USD zoom lens, which was set up on a tripod to ensure it would not change position during the test. Both cameras used ISO 200, center point average metering and were operated in Aperture Priority. The subject in these photos is a scale model of the Lunar Excursion Module (LEM) from the Apollo program.

This set of images compares performance between crop sensor and full frame DSLR bodies. The images in the left column were made with a Nikon D90. Images in the right three columns were made with a Nikon D610. Both cameras used the same Tamron 70-200mm f/2.8 Di VC USD zoom lens, which was set up on a tripod to ensure it would not change position during the test. Both cameras used ISO 200, center point average metering and were operated in Aperture Priority. The subject in these photos is a scale model of the Lunar Excursion Module (LEM) from the Apollo program.

The above illustration allows us to compare the performance of crop sensor and full frame cameras. The first column of D610 exposures matches the settings of the D90 images in the left-most column. Focal length and focal ratio are the same. In most cases, both cameras’ metering systems selected the same exposure. The most obvious difference between the D90 and first set of D610 images is the wider angle of view delivered by the full frame sensor. For the second set of D610 images, I zoomed in to match the effective focal length of the D90. The angles of view of these images closely match the corresponding D90 exposures. The second set of D610 images were shot at f/2.8 and clearly display a more shallow depth of field. For the third set of D610 photographs, I changed the focal ratio to match the depth of field presented in the D90 images. Notice that the exposures for these images are all 1/800-second. They’re longer to compensate for the larger focal ratio.

Focal Ratio is the key to understanding how different cameras, lenses and sensors are able to make good photographs using the same or similar length exposures. Focal ratio determines the length of time needed to collect enough light to make an image having the required surface brightness. For any two cameras operating at the same ISO and delivering the same angle of view, the exposure times will typically be the same.

So, the next time you read or hear a photographer talking about an f/1.4 lens having a larger aperture than an f/2.0 lens, stop and give that statement some thought. If the lenses being compared are a 20mm f/1.4 and a 50mm f/2.0, the 50mm lens will be operating with a larger aperture. The 50mm lens will have a 25mm aperture at f/2.0 and the 20mm, f/1.4 lens aperture will be just over 14mm. However, due to its faster focal ratio, the 20mm lens will deliver more light per square millimeter to the sensor, faster. Because the f/1.4 lens produces a brighter image – an image having a higher surface brightness – the length of the exposure will be shorter.

In photography, the objective is not to deliver the largest volume of light to the sensor. The objective is to deliver the needed intensity (surface brightness) of light to the sensor. Speed is everything and focal ratio is the key.

Now, get out there and shoot!

Bill Ferris | August 2015