Equivalency - Now with pictures!

[Joules]

Introduction

An image says more than a thousand words!

Alright, so show, don't tell! What's up with all this talk about equivalency that seemingly derails every thread around here?

I'll be showing you actual images that illustrate what I am basing my post on, when I participate in these discussion around here. And you are free to just skip right ahead and view these images further down! But, may it help you to get some context on how these images are taken, what they are supposed to show and why they may not show it as best as possible? I believe so. So here's some talk to go along with todays main menu of pictures.

Quick note: I'm writing this in dialog form, but you don't need to feel like I'm addressing you directly or putting words in your mouth with the scentences written from the Perspective of my conversation partner.

 

[Joules]

Motivation

The attentive forum participant may have come across some talk about equivalency - that is, how different sensor sizes, cropping, focal length and f/numbers combine to produce an image. Recent lens releases like the RF 100-500 mm 4.5-7.1 L IS or the f/11 primes or the fate of Olympus, a major player in the realm of micro four thirds, have caused the topic to come up more frequently and show it to be relevant to this forum. Don't think so?

Why should all this dry talk about theory matter, when the joys of photography are in the practical and artistic side of things? I believe a decent understanding of the theory behind a subject is often helpful to properly evaluate offerings and claims made by manufacturers trying to sell you their product. And in photography especially, the theory is also very helpful in realizing an idea you may have in your head, if you have not already build enough intution from lots, and lots of practice to know what your doing by heart.

But on this forum, often this talk about equivalency devolves into a seemingly endless back and forth. Apart from steering away from the primary subject of that thread, there is of course nothing wrong with this. But I get the impression that despite these conversations revolving around a subject with a hard truth based in physics, they don't always end in agreement.

In some instances this is just because of different ways of expressing the same thought or nitpicking. But then there are statements like 'An image taken at 140 mm f/11 will be virtually identical to one taken at 70 mm f/5.6, cropped to match the field of view'. That's either true or false. Yet the discussions often end with the participates just sticking to what they believed to be true when entering it.

So what? This is maybe just a way of justifing the time I spent putting the images together. But in the world we are living in - and more so in the age of misinformation that we are beginning to transition to - it is important to be skeptical. And with the option of just straight up doing the experiments necessary to test ones understanding, it feels irresponsible to put forth potentially deceptive information on the internet.

So, although there is already a lot of information and discussion on this out there, just want to add a little. For one, it is fun to try things out for yourself. And with how often I find myself engaging in these discussions, having a shortcut to point people to also seems nice.

But, please! Don't take any of this as "I'm right, your wrong"! I want to provide some insight into why I'm saying what I do and hope it to either be genuinley helpful in furthering some peoples understanding of photography, or provide a starting point for further discussions that I myself can learn something from.

I will express my understanding of things in a way that sounds like I'm stating it as a fact. Please simply suffix every sentece with 'in my opinion' when reading if you prefer that style of presenting information.

 

[Joules]

TL;DR

What I believe to be common misconceptions (statements exagerated for effect) :

• Using a teleconverter yields wildly different results compared to just cropping!
• f/4 is f/4, no matter what sensor you use it on or how much you crop it!
• High ISO values are the devil, adding all that noise into my images!
• Want that sexy 'tele compression' effect? Use a long focal length! Nothing else will get you that!
• Those teeny tiny pixels on modern sensors are hurting my low light performance!

The images I've got going here aren't cut and dried evidence of the contrary - But they should at least give you some food for thought if you believe any of the above statements (or a more moderate version of them).

 

[Joules]

Shortcomings

When I show some images of a real scene here, they won't quite match what the theory predicts. Is the theory wrong, then? I don't think so! There are a lot of factors influencing how an image looks. I am unable to control all of these with the limited time and equipment I have. Most notably, some things to consider:

• The f/number and focal length printed on a lens spec are not perfectly accurate in describing a lens' actual properties. My EF-S 55-250 mm 3.5-5.6 may be something like 241 mm f/5.73 at the long end, for example.
• As the focus distance changes, so do the effective focal length and f/number. This is especially apparent near the minimal focus distance.
• The information displayed in the EXIF are only approximately what's actually going on. For example, the reported focal length on my lens skips from 143 to 135, without any values in between. So what I will later call 140 mm is actuall 143 mm, according to the EXIF, but I kept turning the ring a bit further.
• The light I'm using is artifical light, mostly produced by LEDs. So it does flicker, although I tried paying attention to this using only appropriately low shutter speeds, it likely has some impact on the images dealing with noise.
• My personal camera is an 80D, and while it is so, SO much better than older Canon Sensors - it still is a Canon sensor, and not of the latest generation. Meaning it suffers from more banding and other sources of noise than the latest and greatest sensors found in such cameras as the 90D/M6 II, 1DX III, R6 or R5. As future sensors get ever closer to the theoretical limits of phyisics, this theory will apply to practice with ever smaller asterisks.
• The zoom lens that I am using extends when zooming. This causes there to be little differences in perspective that I have not compensated for by moving the camera.

You see a flaw in my arguments, or don't find my evidence convincing? Great! Please offer your explanation of what the images show, challenge the ideas or run your own experiments and share the result! Participate! That's how science works and gives all of us a chance to learn and improve our understanding.

 

[Joules]

Noise

Noise is that fuzzy stuff that shows up in my pictures when the lighting conditions are not ideal, right? So what is it and where does it come from?

Noise is just a variation in the pixel values that does not reflect the actual properties of the subject. So, it is pixels being brighter or darker than you expect them to be, given the object that they get their color from.

There are two main types of noise. One is the noise that is generated in your camera. The temperature the sensor is at during the exposure is responsible for part of that noise, called dark current noise. The lower the temperature, the less noise is added through this. Heat is just a form of energy and some of that energy can take the form of charge inside a pixel. Another source of noise are the analog electronics in the camera themselves. They are not perfect, and so they create little errors in the data before it is converted to a digital format that can be made much more resiliant against corruption caused by our messy physical world.

Let's have a look at some of this noise. I took a series of images with the lens cap on and the viewfinder covered. I used both my 80D and a friend's 90D for this, so we can have a look at the differences between an older and newer sensor of the same size. Lens, aperture and shutter speed are all the same between these shots: Sigma 35mm 1.4 Art, f/2.8 (doesn't really matter with the lens cap on), 1/50s. Same whitebalance for each. Shots taken over very small amount of time, indoors. So the temperature is very similar. All the noise in these images is caused by this thermal energy or the camera electronics. The upper two rows show the images unedited - Luminance and color noise reduction in Lightroom turned off, no sharpening, no profile corrections. This will be true for all my images. The lower row is normalized in brightness, so that we are comparing apples to apples. The number of stops the exposure was pushed in Lightroom is shown as (stops) at the top of each column.



Without any noise, these images would just be pure black, as there is absolutely no light. Notice that isn't the case though and especially with the lower ISO shots that had the exposure raised, the dark current and read noise are really visible.

But wait, how is it apples to apples comparing images where the exposure was raised by different amounts in post?
Well, the only difference in these shots is the selected ISO. And what does ISO influence? The brightness of the image. So if we want to compare images at the same brightness, the ones taken with a lower ISO have to be brightened in post. Doing that does not add any noise, it is a purely digital process. Whatever noise we see is already in the image file, you just couldn't see it previously because it was so dark!

These are the aspects that camera manufacturers have control over and have spent generations of camera bodies to improve. Notice also how little of it there is in the 90D images. They have improved so much now, that for many situations, these types of noise actually aren't the limiting factor for low light performance anymore.

That would be the second kind of noise: a property of light itself, called shot noise. To me, this was initally very unintuitive. But yes, light is actually noisy. Even a perfect sensor, created by the all powerful religious being of your chosing, would not be able to create a noise free image unless said being also altered the properties of light. An analogy you'll often find on the internet is comparing the electrons that are responsible for your image to raindrops, and the pixels to buckets.

As the rain is coming in the form of discrete drops, not all pixel buckets will have the same amount of water in them at all times. But as the amount of water (light) increases, these little differences become less and less apparent. How these little difference compare to the total amount of water (light) is what the signal to noise ratio expresses. I won't go into the details of how it is calculated, since there's already such a great source for this out there: Jon Rista on SNR
Jon Rista goes into great detail on the mathematics behind it in the context of the most low light photography there is: astro. I believe he also is a former member of this forum (jrista) who posted absolutely magnificient images.

What this means though, is that if we ignore the noise generated in camera, what ultimately determines how visible noise is in the image depends on how much light this image contains. What determines how much light goes into an image? Three things: The amount of light per area and time that falls onto the sensor, the area of this sensor and the time over which light is gathered.

But wait, a small pixel has a lesser area than a large one, so it gathers less light. That has to matter, right?
Well, yes. If you look at individual pixels. But when looking at an area of multiple pixels, like an image, all the pixels in it are averaged by the software that produces the image you are looking at on your screen. Or in the case of a print, your eyes handle that.

And ISO? I see a lot of noise in my images when I use high ISO values!
Yes, that is to be expected - you usually will raise the ISO when the amount of light you gather is not producing the desired brightness and you can't use a larger aperture or longer shutter speed, right? So, in other words, whenever you use a larger ISO, you are capturing a smaller amount of light than when using a small ISO. But it is not the ISO itself that is introducing the noise into your images - The small amount of light is responsible for that!

Alright, so are you saying ISO doesn't matter and I get the same image quality as long as I keep the f/number and shutter speed the same?
Basically, yes. So let's do just that and have a look. Same thing as before, Sigma 35mm 1.4 Art, f/2.8, 1/50s, no noise reduction, sharpening or profile corrections in Lightroom. This time, the lens cap's off and we're looking at a small crop (the same relative crop for each) showing a dimly lit wall. The image is out of focus so that the texture of the wall doesn't show up. Upper two rows are unedited, lower to pushed by the amount stated in the brackets at the top.



Notice that the normalized 90D images look very similar, regardless of ISO! And that for the 80D, pushing digitally in post rather then selecting a higher ISO to achieve the desired brightness actually results in a much more noisy image! In this crop, it is not visible, but there's also a lot of banding in the raised 80D ISO 100 shot when viewed at full size. Yikes!

So in other words, if you don't want your image to look noisy: Gather as much light as possible using a long shutter speed and wide aperture. If you can't achieve your desired brightness that way, crank up the ISO in camera as far as necessary. You will get worse results if your camera isn't one of the very recent models and you have to brighten in post. Also be aware that higher ISOs have lower dynamic range though. So there absolutely is a time and place for shooting an image that looks to dark in camera and boosting in post, if you want to preserve highlights. Especially with how little read noise there is in these modern sensors.

Okay, but what about the sensor size then? When my image comes from a smaller physical area, it has less total light in it. Does cropping or shooting with a smaller sensor really give the same effect as gathering less light by using a shorter shutter speed?
Let's try just that. Same thing as before, no NR, sharpening, same aperture and lens, looking at a (almost) uniformly lit, out of focus wall. Only the 80D this time, as I had to give back the 90D by the time I took this test. All shots have the same brightness, of course. So, to make the noise more apparent, I pushed them all by 4 stops in the lower rows. This is as far as I can push the 80D before banding shows up. The bottom row shows a section of the middle row that is cropped to compensate for the difference in total light. So, no crop at all on the left most image, cropped to half the area in the second one from the left, 1/4 the area in the third one, 1/8 the area in the forth one, and so on. So in the bottom row, all images are made up of the same amount of light.



Things to note here? First, the color goes off the rails as the light drops. Not sure what's causing that. But apart from that, noise in the bottom section looks really consistent between all of these. Which is what I would expect based on the three main factors I named earlier. After all, as we go from left to right, the exposure times gets cut in half, but the area doubles, resulting in the same amount of light. And so, why would the noise be any different?

 

[Joules]

Perspective

(Will edit this post later to add a few words about this later. The message is just this: There's no such effect as tele compression. That's just differences in Perspective due to how far you stand away from a subject when using a telephoto lens. Cropping will give the same look)

 

[Joules]

Equivalency

Summary: You can take to images with different focal length and f/number settings. When the quotient of focal length divided by f/number is the same in both cases, the images will look virtually identical when the wider one is cropped to match the other's field of view. That's the theory at least.

Example:

Here are two shots. Left is 194 mm f/11 1/5 s ISO 640. Right is 100 mm f/5.6 1/5 s ISO 160. These are the settings according to the EXIF, meaning they are just approximations.


Cropped to the same FoV and overlaid to emphasize the (lack of) difference:


To refresh our memory on what a real visual difference looks like, here is a crop from these two images, with a third one taken at 100 mm f/11 added:


Notes about test methodology:

Due to using the inexpensive EF-S 55-250 mm IS STM for this test (my only other zoom is the Sigma 150-600 mm C), I had to take multiple exposures around the 200 mm with little increments to find one that matches the single '100 mm' shot I took. I put that in quotes, as the lens jumps from reporting 89 mm to 100 mm to 109 mm when zooming. I took one image with the indicator positioned the middle 0 of the 100 printed on the barrel. And I took 28 additional images around the 200 mm mark. Of these, the '194 mm' presented above comes closest.

Takeaway: Zooming and cropping to the same thing with different means. Note that using a smaller sensor format is exactly the same as cropping, only done during the image capture if you will. Attempting to show this using a very inexpensive EF-S lens is more difficult, but you can easily do the experiment yourself if in doubt. Consider the shortcomings I shared above if you want to do this. And please share your results if you have the time

Note: I edited this text to make it more concise. The previous version:

Spoiler: Original text

Okay, noise is all about how much light the image contains. And a smaller sensor or smaller f/number cause less to be gathered. Focal length is supposedly not doing that much for how the image looks, as it is the distance between you and the things in the image that determine how large they are relative to each other. But saying that just because the amount of light balances out, can you really say using a fast, short lens on a small sensor is comparable to using a slower, longer lens on a larger one?

Glad you asked. I happen to have just the set of images prepared to take a look at this. Let's begin with four different images, all uncropped. I usually don't lens caps and wall so much, so why not look at a real scene for a change. Just some christmas decorations in the living room, taken on the 90D, the settings are in the picture. No crop for now. Images with the same f/number and ISO are next to each other horizontally.



Nothing surprising here, I'd say. A longer focal length results in a smaller section of the scene being visible. And a smaller f/number results in a more out of focus background. This is clearly comparing apples to avocados. So I'll crop the wide shot to 1/4 the size, to match the longer shot's field of view.



Alright, that doesn't look all that different anymore. Let's actually swap the images on the right, so that we can compare 140mm f/11 to the cropped 70mm f/5.6 directly.



Okay, I'm looking at it. If you're saying to me the two upper images look the same, may I recommend you get your eyes checked?
Fair point, they don't look identical. I've given the shortcomings of my testing at the beginning. But tell me, what would you have expected them to look like? If you ask me, they are more similar than they are different. Especially if you compare them with the other shots.

Also, with regard to noise: The crop I introduced discarded 3/4 of the light in the shot, so really, the exposure time has to multiplied by 4 to compensate for this. So let's end with a closer look on that, where all are cropped to show the same image section in detail:



The lower and middle image should have settings that cause there to be the same amount of light in this section, and indeed, I see the image quality as very, very similar.

 

[Joules]

Conclusion

To be continued ... (music starts)

 

[Joules]

As you may have guess, this took some time to put together (and it isn't finished yet ). I would appreciate some feedback, so that the time will at least feel well spent

First thing to note myself: As usual, the pictures got butchered on uploading them here. I may have to upload them somewhere with support for higher resoultions when I get around to it.

 

[Maximilian]

Thanks for all that effort. I think I'have to read through it, when my mind is a little bit fresher

 

[Ozarker]

As you may have guess, this took some time to put together (and it isn't finished yet ). I would appreciate some feedback, so that the time will at least feel well spent

First thing to note myself: As usual, the pictures got butchered on uploading them here. I may have to upload them somewhere with support for higher resoultions when I get around to it.

Great effort (and it is appreciated), but somehow this is not what my OP was about at all. My OP was really about whether one would rather use a crop or a TC, seeing as though a TC changes the f/stop (resulting in slower shutter speed and/or higher ISO). F/11 vs f/16. I'll take the crop in such a situation every single time. My comment had nothing at all to do with equivalency or not. I specifically said that equivalency is not part of my deal. The RF 800mm f/11 probably is not going to be used to take indoor photos of Christmas decorations, and certainly not with a TC. If I am shooting birds or soccer players at f/11, that's dark enough for me. That's a slow enough shutter speed for me. That's a high enough ISO for me. Equivalency is not part of the argument, at least, not for me. Now, it may very well be a part of the argument when the TC takes an f/2.8 combo and turns it into an f/5.6 combo. Then I can see value in the debate. You took photos of a static subject. Now let's try f/11 vs f/16 (f/16 with a TC vs cropped image) on a fast moving bird or soccer player that requires faster than 1/20 sec shutter speed. Much good will towards you, not criticizing at all. BTW: Did you use a TC in the photos? In my experience (Canon EF 2x III) the TC degraded IQ differently than just changing f/stop in camera. I could have had a poor copy of the TC or been terrible at AFMA. I personally think the comparison should be between photos that use a TC (at f/16) and don't use a TC (at f/11). What we are missing here is what a 2x TC does to the photos, and that's a big deal.

 

[Joules]

Great effort (and it is appreciated), but somehow this is not what my OP was about at all. My OP was really about whether one would rather use a crop or a TC, seeing as though a TC changes the f/stop (resulting in slower shutter speed and/or higher ISO)

Thanks for the comment. I did mean to produce the images for a while now, as it felt problematic to always go into conversations in this stuff without anything tangible to back up my point. So, don't feel criticized here personally! Part of why I replied to you in the other thread was to have at least somebody look at this before it gets buried in the forums

Though I don't quite know what you are saying with regards to a TC here.

I do not own one, so no testing of that will come from me. But, that's what me using my zoom at 70 mm 5.6 vs 140 mm 11 (could have used a 2X TC here, rather than actually zoom) was meant to show. Very different settings, but when you compare them cropped, at the same shutter speed, with the only difference being ISO - you get a very similar image. In theory, the same image.

That essentially is very much supporting your point that cropping is superior to using a TC! It produces virtually the same image in terms of noise, DOF, FoV, diffraction and so on, without the disadvantage of potentially degrading detail and flare resistance due to extra lens elements. That is, if your sensor is high resolution enough to resolve enough detail to allow such a deep crop in the first place, of course.

If I am misunderstanding your point or you see a problem with my argument, feel free to let me know!

 

[Ozarker]

Thanks for the comment. I did mean to produce the images for a while now, as it felt problematic to always go into conversations in this stuff without anything tangible to back up my point. So, don't feel criticized here personally! Part of why I replied to you in the other thread was to have at least somebody look at this before it gets buried in the forums

Though I don't quite know what you are saying with regards to a TC here.

I do not own one, so no testing of that will come from me. But, that's what me using my zoom at 70 mm 5.6 vs 140 mm 11 (could have used a 2X TC here, rather than actually zoom) was meant to show. Very different settings, but when you compare them cropped, at the same shutter speed, with the only difference being ISO - you get a very similar image. In theory, the same image.

That essentially is very much supporting your point that cropping is superior to using a TC! It produces virtually the same image in terms of noise, DOF, FoV, diffraction and so on, without the disadvantage of potentially degrading detail and flare resistance due to extra lens elements. That is, if your sensor is high resolution enough to resolve enough detail to allow such a deep crop in the first place, of course.

If I am misunderstanding your point or you see a problem with my argument, feel free to let me know!

Here's a shot of the post that started all this. Somehow, people thought it (what I wrote) had something to do with equivalency. My point was that I would not use a TC if I was already at f/11... I'd rather crop. Somehow, people thought this was about equivalency. It isn't, and it wasn't. @usern4cr made a reference towards equivalency. I preferred to stay out of that. If I had an f/11 lens it would still expose at the same ISO and shutter speed whether I crop it or not. Not so for a lens with a TC attached. The TC would affect f/stop (of the combo), shutter speed, and ISO. Background blur is not the issue at those focal lengths, for me. While I see the point of your test, it does not take into account IQ degradation from a TC. Neither do the "equivalency" arguements.

 

[Bdbtoys]

Equivalency

View attachment 194308
Alright, that doesn't look all that different anymore.

What am I missing with this comment? It looks like there should have been a point made here. The 140mm clearly has more bokeh effect than the 70 cropped.

 

[Joules]

What am I missing with this comment? It looks like there should have been a point made here. The 140mm clearly has more bokeh effect than the 70 cropped.

You are right, it absolutely does.

A post further up titled shortcomings lists reasons why this is the case in my opinion. Essentially, we can't trust what is written in the EXIF or lens barrel. So I am comparing 'roughly 140mm, roughly f/11' to 'roughly 70mm, roughly f/5.6' here. Hence, I would expect to get 'roughly the same image'. With my personal margins of error, that is the case.

Mind you, this is a very inexpensive lens I'm using here. I'd love to see it done with 70-200 2.8 at 80mm 4.0 vs 160mm 8.0, for example. Ideally, with properly measuring the focal length, rather than trusting any reading.

The point really is this: which of the four images shown to you find most similar do each other?

Edit: The alternative test methodology is of course taking many images with slightly different focal lengths around 70 and 140 mm and finding the pair that look actually identical, and then looking at the EXIF to determine how far off the reporting is.

I guess I may still do that, as it should not take to much time when simply zooming while shooting a burst. And you are of course right, given how much fuzz I made with all that text I should present more conclusive evidence. If the result is not obvious to the reader, it is a poor proof.

 

[Joules]

What am I missing with this comment? It looks like there should have been a point made here. The 140mm clearly has more bokeh effect than the 70 cropped.

I have updated the post for you. Made a point and provided pictures that require less mental interpolation to support said point.

The real point here is that I find it makes life easier when you can stop thinking about cropping, zooming, sensor sizes, teleconverters and so on as very similiar in effect and focus instead on the nuances in which they differ.