What Is Equivalence?

Equivalence was one of several third-rail topics of bitter dispute...erm, discussion on DPReview. As I write this, I'm smiling because it needn't have been the case. In this post, I am introducing the beginning photographer to equivalence. This post is for those who may have heard about equivalence but aren't quite sure what it is or if it matters. This isn't intended to be the final word on the subject. As mentioned, this post will be an introduction.

I'm going to begin by telling you what equivalence isn't. It is not a tool for determining which camera format is best. If you're into digital photography, you're probably aware that digital cameras can be built around sensors of different sizes. Each size or format has its own name, such as full-frame, APS-C, micro four thirds, and 1-inch, among others. The size of the sensor has an effect on the kind of image a camera makes at a given collection of settings. This is something you're probably aware of. If you've done photography with a smartphone camera, you've probably noticed it's photos look pretty different in comparison with the photos you've been making with your dedicated digital camera. The smartphone camera is probably built around a sensor that's about 1 cm in size. The dedicated camera's sensor is much larger. The difference in the sizes of the two sensors is a big reason for the difference in how those photos look.

If you take anything away from this post, I hope it's the following: equivalence is a tool for determining which settings can be used by different format cameras to make photos that look the same; that are equivalent. Note that the TLDR summary statement doesn't say anything about determining which of the formats is better. That's because equivalence is not intended for that purpose.

Keeping all that in mind, let's get started. Two photos are equivalent if they share the following six properties:

Perspective
Framing
Exposure Time
DOF/Diffraction/Total Light Captured
Lightness
Display Size

Let's make sure we have a shared understanding of what those terms mean. By perspective, I am referring to the place from which the photo was made. If two photos are made of the same subject from the same spot, they've met one of the six properties for being equivalent.

By framing, I am referring to the angle of view captured in a photo and the position of compositional elements within the frame. You'll see a good illustration of this in a bit but, for now, I'll summarize by saying that if the two photos capture the same composition from the same point of view, they've met the second of six properties for being equivalent.

Exposure time is a reference to the shutter speed used. This is important because shutter speed determines how movement in the frame will be rendered. It's the setting that determines how much motion blur there will be. If two photos are made with the same shutter speed, they've met the third of six criteria for being equivalent.

Next, there's that three-part property, DOF/Diffraction/Noise. DOF is an initialism for depth of field. In layperson's terms, think of this as the distance within the photo from the nearest to farthest elements that look to be in good focus. The photos I share will illustrate this. Diffraction is a property that determines the resolution or sharpness of details in a photo. Noise is a reference to another property of a photo. As you know, a photograph is made when light is delivered to a light-sensitive medium such as a modern camera sensor. Noise is a naturally occurring property of the light delivered to and captured by the sensor. The more light used to make a photo, the less prominent noise tends to be. The less light used to make a photo, the more prominent noise will be. The size of the opening through which light passes to get to the sensor - the lens's aperture - has a lot to do with these three properties. If depth of field (DOF), diffraction, and noise in the photos are the same, they've met the fourth of six properties for being equivalent.

Lightness may sound, at first, like it's the same thing as how much light is used to make the photo. It's actually a different property. The screen you're looking at while reading this post illustrates what is meant by lightness. You may be seeing a display with black text against a gray background which, itself, is framed on either side by a white background. The white background is lighter in appearance than the black text. In fact, those elements probably define the lightest and darkest tones in the screen display. The gray background is reasonably close in tonality to what is known in photography as middle gray or 18% gray. It's halfway between black and white in tonality. This is what is meant by lightness. It's not the amount of light used to make the photo. It's the tonality of the photo. If the two photos have the same tonal lightness, they've met the fifth of six criteria to be equivalent.

The sixth and last property shared by equivalent photos is display size.By this, I'm referencing how large a photo looks to you. The factors that determine this are the actual size of the photos and your perspective as the viewer looking at the photo. If both photos are the same size and are viewed from the same perspective, they'll have the same display size. That, along with the other five properties, would make the two photos equivalent.

The table is now set so, let's look at a couple of photos.

This photo was made using a Fuji X-T20 with an 18-55mm f/2.8-4 zoom lens at 41mm, f/8, 1/8-second, ISO 1600

This photo was made using the same Fuji X-T20 camera and 18-55mm zoom lens at 21mm, f/4, 1/8-second, ISO 400

I invite you to view them full size and compare them for composition, rendering of movement, depth of field, detail, noise, and lightness. While you're doing that, I'll share some details on how the photos were made and why I chose the various settings used to make them.

Both photos were made with the camera on a tripod. The tripod and subject were kept in the same positions in my living room for both photos. The photos share the same perspective.

The second photo was cropped to match both the angle of view and composition of the first. Both photos were made using the same 1/8-second shutter speed. I'll discuss the reason for using that focal length toward the end of this post. Here's what the uncropped photo looks like.

This is the uncropped version of the second photo.

Let's compare and discuss the first two photos. They were made from the same perspective, share the same angle of view, and were made using the same shutter speed. The first three properties of equivalent photos have been met. Check, check and check.

Next, we get to DOF/diffraction/noise. Depth of field is largely determined by the distance of the camera from the subject and the size of the lens's opening; its aperture. Let's do some simple math. The first photo was made at 41mm, f/8. The f-stop is a setting that can be used to determine the lens's aperture. If we divide the focal length by the f-number, we get (41/8=5.1) a 5mm aperture for the lens. The second photo was made at 21mm, f/4. Dividing the focal length by the f-number, we get (21/4=5.3) a 5mm aperture for the lens. With the lens having the same aperture for both photos, depth of field (DOF) will be the same. Diffraction will also be the same.

As for noise, we've already discussed that the visibility of noise in a photo is determined by how much light is used to make the image. Let's consider that issue in the context of these images. The total light delivered to the sensor is a product of exposure times the surface area of the sensor. Exposure, in this context, has a specific meaning. It refers to the brightness (intensity of light) of the scene per unit area as projected by the lens on the sensor. Exposure is determined by the available light in the scene, f-stop, and shutter speed. The scene had the same available light for both photos. The same shutter speed was used to make both images. The first photo was made at f/8 while the second was made at f/4. The larger f-number tells us a lower exposure was used to make the first photo; two stops lower. Each difference of one stop represents a 2x difference in light. However, the full area of the sensor was used to make that first photo. The uncropped first photo used a sensor 2x the size of the second in width and height. That's 4x the surface area compared with 4x the exposure. They cancel out.

The net result of all this is that both photos were made with the same total light. Therefore, they have the same noise visibility. With DOF, diffraction, and noise the same in both photos, the fourth shared property has been met. Check.

As just mentioned, the first photo was made with a lower exposure. That photo was also made at ISO 1600, which allows it to match the second photo in lightness. The second photo was made with a greater exposure but at ISO 400. Since both photos have the same lightness, the fifth property of equivalent photos is met. Check.

I exported both photos at 2500 pixels in width with their aspect ratios preserved. If you've viewed them at their original sizes, you've seen the images displayed at the same size and distance. The sixth and last of the properties for equivalent photos has been met. Check.

The first two photos are equivalent. Note, that looking identical is not a requirement for two photos to be equivalent. In this comparison, we can see the lens characteristics at the different focal lengths used are subtly different. The crop of the second photo was done manually and is not a perfect match in composition with the first. The photos have subtle differences in appearance as a result. Still, they share the six required properties and, therefore, are equivalent.

Since the first photo was made with a sensor effectively twice the size and four times the area of the second, the two photos are representative of equivalent photos made with full-frame and micro four thirds cameras. A micro four thirds sensor is half the size and one-quarter the area of a full-frame sensor. That's exactly what we have here with these two photos. The first photo was made with a sensor area four times the size of that used to make the second.

Viewing and comparing the two photos, I think it's fair to say that look very much the same. There are subtle differences but they are minor in comparison with the overall appearance and impression of the images.

OK, so why is equivalence important?

As stated earlier, equivalence is a tool for determining which settings can be used with different format cameras to make equivalent photos. While different format cameras don't always produce equivalent images, you now know that it's possible. The potential exists for different format cameras to perform the same. The next time you are in the market for a new camera, you'll probably have several criteria in mind that you would like it to meet. You might have a budget set for the purchase. You may have a particular genre of photography in mind for the camera. You may have a preference for a camera of a certain size and weight. You may have a preference for a long focal length or wide angle system.

With your purchase criteria in place, equivalence empowers you to consider and compare different format cameras to find a specific model that best meets your needs. I don't know - and with respect, frankly, I don't care - which format camera you end up choosing. My goal in making this post, is to provide you a tool that can be used to help identify the camera that will best meet your needs...whatever format that camera happens to be.

Any discussion of equivalence should have a link to the ultimate article on equivalence:

www.josephjamesphotography.com/equivalence/

I agree.

And here's an article that discusses the limitations of equivalence.

blog.kasson.com/the-last-word/format-size-and-image-quality/

Thank you. Both links are excellent additions.

Bill,

Thanks for the informative post.

Here are links to two DPR articles by Richard Butler, for those who might want to do some additional reading.

www.dpreview.com/learn/2799100497/equivalence-in-a-nutshell

www.dpreview.com/articles/2666934640/what-is-equivalence-and-why-should-i-care (with 2500 comments!)

You're a brave person :-)

Sherm

Those are excellent resources. Thanks for posting.

I found that thinking about equivalence was very helpful to me as a beginner who started out with a camera with a 5.7-22.9mm F2.8-4.8 lens. If I didn't know anything about equivalence I probably would have been lost, even before I bought the camera.

In the standard exposure model, f/2.8 is equivalent to f/2.8. In the equivalence model, they are not.

Which is why large formats work best with lots of light.

The equivalence model is a part of integral exposure model.

I was just making the point that aperture is not f-number. In any model, exposure is light per unit area.

Your last sentence appears to say you need different apertures on different formats to get the same DOF, given the same FoV. Is that what you meant?

The standard model says f/2.8 is f/2.8 and stops there. Equivalence looks at effects, such as noise (a function of total light on the sensor) and DOF, which are not the same across formats at the same f-number, all else being equal.

Yes, if your concern is light per unit area than f/2.8 is always equivalent to f/2.8. If your concern is what the resulting image will look like (in respect to depth of field and image noise) then f/2.8 on one sensor size will give different results than f/2.8 on a different sensor size.

It's all about whether you are talking about implementation details (light per unit area on the sensor), or the what results you will get.

A light meter used properly will tell you the exposure you need -- more or less - independent of format. It's up to you to pick equivalent focal lengths and f-stops if you want to make two images that are similar with two different formats.

The light meter knows nothing about DOF, angle of view, or diffraction.

A light meter is used to determine exposure when a specific exposure is wanted (such as someone shooting slide film or JPEGs to be sent from the camera to someone else, with no ability to alter brightness after exposure). The meter doesn't care about total light.

While it's true that f-stop and aperture are often used interchangeably in informal discussions of photography, it's also true that the lens's aperture diameter (virtual aperture diameter, if you prefer) is a different physical quality that plays an important role in determining the depth of field of the image projected on the sensor.

A big reason why this and other forums have beginners' questions areas, is to provide an environment where a photographer can expand their understanding of how a camera works. When it clicks that f-stop determines exposure but the aperture diameter determines depth of field - and thus how a photo made at f/5.6 with one camera can have a much shallower depth of the field than a photo made at f/1.8 with a different camera - that's an empowering moment for a person. That's knowledge that empowers the photographer to have more control over both the light used to make a photo and the depth of field captured in that image.

Equivalence helps a photographer understand that it's possible to make the same photo with different format cameras. It's helps a photographer understand that exposure is the not the only light-related factor and f-stop is not the only lens factor to take into consideration when making a photo. That knowledge then empowers a photographer to take more control over the image-making process.

A light meter can be a useful tool. It is also useful to know the actual focal length of the lens, and the aperture diameter.

Taken in isolation, none of these things individually tells you much about the final image.

For instance, a 20mm lens might provide a wide, normal or telephoto angle of view, depending on what camera it is mounted on. Now we can "normalize" and talk in terms of the equivalent focal length on a full frame camera. However, a 20 mm lens is always a 20mm lens, no matter what the sensor size. What's different is how it affects the image.

Similarly, f/2.8 tells us the ratio of the focal length to aperture diameter. Both are physical things, and don't change with sensor size. However, f/2.8 might provide shallow or deep depth of field, depending on sensor size. If you think it is reasonable to normalize focal length to the full frame equivalent, you should be open to the idea of normalizing f/stop the same way.

A light meter tells us about the light on the subject. At any particular light level, we can choose camera settings that yield a low or high exposure. Often we want a higher exposure in order to minimize noise. Typical light meters allow us to set a target exposure (by setting the ISO that corresponds to that exposure), and the meter can suggest aperture/shutter combinations that will hit that target exposure. However, this in isolation tells us nothing about image noise. The same exact exposure can produce a noisy image, or a visually noise free image, depending on sensor size.

Again, it all boils down to whether you want to discuss implementation details, or what the resulting image will look like.

My experience using an external light meter is limited to the context of lighting a space for a video shoot. I have none using a handheld light meter for photography. However, I use the in-camera meter of my digital cameras every time I'm out doing still photography.

I treat the in-camera meter as a lightness meter. It's a reference for confirming that the photo being made will have a pleasing lightness. It's not what I rely on to confirm a good exposure or that I'll be putting enough light on the sensor to make a quality image.

I use ISO as a reference - an indicator - of the exposure being delivered to the sensor. I'm often at ISO 400-640. If that ISO delivers an image having a pleasing lightness, my experience working with photos in that range of ISOs, gives me confidence the exposure delivered to the sensor and total light used to make the photo will be adequate to the goal of producing a quality image. There is a caveat in that assessment. It assumes I won't be significantly cropping the photo in Lightroom Classic. The deeper the crop, the less light ends up being used to make the finished image. Noise can become quite prominent.

A standard one doesn't, but nobody forbids to write an app for a phone, or to make a DIY one, costs very little - and it can even serve as a spectrometer ;)

Beginners question, what is equivalence in practice as I see it with few words:
(but are equivalence for beginners? ;-)) are beginners reading this

Smaller sensor can equivalence bigger sensor quality "in real world" only if you need huge depth of field and high shutter speed.

Example: seascape with frozen waves in storm 1/2000 sek aperture 16 FF (very high ISO). You can equivalence do that with APC also or 1" or mobile phone.
To get favour of bigger format, ie collecting more light, you have to use slower shutter speed, but then the waves will be blurry.

You'd use f/10 on a 1.6x-crop sensor (Canon APS-C) and 0.625x the focal length for the same image. You can change shutter speed freely on either. Change to 1/1000 on either camera, and you get twice as much total light, but total light is the same with the same shutter speed. No difference between the two systems, in total available light, with the same shutter speed.

good explaining:-) yes, f/10 on 1.6crop, about f/5.6 on 1" and about f/2.0 on mobile phone?, same shutter speed, same total light as FF f/16

If beginners reading (I know you are not beginner:-) : the other direction are more difficult, if we want narrow dept of field, like f/1.4 on FF. Equivalent lens doesn't exist on tex 1"sensor. FF can do everything smaller format can, but not in the other direction. A yet disadvantage for smaller cameras with smaller sensor are they have to use mostly "wasted high shutter speeds" in good light for ordinary photography. Stupid example: using 1" camera and picture of something that doesn't moving in sunlight you still have to use shutter speed of 1/1000 on lowest iso! wasted shutter speed and IBIS/VR doesn't give us anything. In the end the only advantage for smaller cameras are weight. Sorry for my English, its not my first language

At the same angle of view, same aperture diameter, and same shutter speed, you will get essentially the same image, independent of sensor size.

Aperture diameter is the physical focal length divided by the f/stop. A 2X crop body with a 25mm at f/2 offers a 46° angle of view and a 12.5mm aperture diameter.
A full frame with a 50mm lens at f/4, also offers a 46° angle of view and a 12.5mm aperture diameter.

If both are at the same shutter speed, the resulting images will be essentially the same. Same depth of field, same framing, same diffraction, same overall image noise, and same motion blur.

Equivalence helps one determine how to take the same photo across a wide range of sensor sizes.