Does 16.16MP FF cropped = 10.1MP xxD image? Where's the reach?

I'm still trying to figure all of this crop vs FF jumble. Everyone says they like the "reach" of a 1.6 crop sensor. So, if we took two images of 1 subject at the same distance using two different cameras

1. Full frame 16.16MP (hypothetical)
2. 40D 10.1MP

Would cropping the hypothetical FF image to the same dimensions of the 40D image yield the same effective result in image quality? To me it doesn't seem you like gain any reach in your photos using a 1.6x crop camera. It's more like you just squandered away some of your image. The reason I chose a 16.16MP sensor is because I'm trying to keep the argument of squeezing light onto photosites ineffectively out of the question.

Cropping hypothetical 16.16MP full frame image to 1.6x crop size will give you 6.31MP image.
You have to devide the full frame size by 1.6x1.6 = 2.56.

I believe crop sensors are smaller though:
40D 22.2 x 14.8mm 5.7µm
Canon EOS 1D Mark III 28.1 x 18.7mm 7.2µm

So since the projected image onto the sensor is smaller for the crop sensor, they use a smaller sensor. I think you can make your argument if the sensors are the exact same, but manufacturers build sensors differently for crops than they do for FF. Your argument then is invalid.

I still don't see where "reach" comes into play here, though. I still get the impression that a cropped FF image would certainly rival a cropped sensor's uncropped image.

it really is a perceived zoom, and not a true zoom. it it true what you say about really just losing the edges of an otherwise larger image.

to get the same framing on a full frame camera, you would have to use a longer lens

the image just appears as if you were standing nearer than you actually were, because you lose the edges.

This "stolen" from the luminous landscape website:

Hope it helps. Really, with that many pixels, you can crop to a 1.6 factor and not lose much pixel density as far as making a good print.

drPheta wrote in post #5563783
I still don't see where "reach" comes into play here, though. I still get the impression that a cropped FF image would certainly rival a cropped sensor's uncropped image.

You would get the same picture by cropping a FF shot but not the same resolution. Crop cameras generally have a greater pixel density than their FF cousins. So, in a round about way, crop cameras can be said to give more reach or more accurately, more pixels on target.

jra wrote in post #5563804
You would get the same picture by cropping a FF shot but not the same resolution. Crop cameras generally have a greater pixel density than their FF cousins. So, in a round about way, crop cameras can be said to give more reach or more accurately, more pixels on target.

that pretty much sums it up right there.

You don't gain any reach, but due to differences in sensors (pixel density and what not) and due to the fact that you enlarge an APS-C image more to match a comparable full frame image display size it appears you get more reach. Misuse of 'reach' like 'crop' cause all this fun.

Vermin87 wrote in post #5563763
So since the projected image onto the sensor is smaller for the crop sensor, they use a smaller sensor. I think you can make your argument if the sensors are the exact same, but manufacturers build sensors differently for crops than they do for FF. Your argument then is invalid.

As its a hypothetical sensor its perfectly valid, it wasn't an argument it was a question (and response based on the hypothetical question).

drPheta wrote in post #5563783
I still don't see where "reach" comes into play here, though. I still get the impression that a cropped FF image would certainly rival a cropped sensor's uncropped image.

Not at the 2 resolutions in question (6MP from cropped FF vs. 10MP from uncropped 1.6x). That's a significant resolution difference, although how significant depends on print size.

The extra reach is no illusion. It might be a misnomer, but the benefits are real. Within certain other limits (noise performance, diffraction, etc.), the more pixels on target the better, and 1.6x crop cameras currently have higher pixel resolution than 1.3x and FF cameras, resulting in a final image with more pixels on target in focal-length-limited situations. This advantage might eventually disappear if the current trend continues, with FF sensors coming closer and closer to the pixel density of 1.6x crop sensors.

Yohan Pamudji wrote in post #5564091
This advantage might eventually disappear if the current trend continues, with FF sensors coming closer and closer to the pixel density of 1.6x crop sensors.

this will also increase digital noise though, so it's not necessarily a good thing.

The crop benefit is real, but only so long as you are planning to actually crop down from FF to a 1.6X image size all the time. In such a case you are really better off getting a higher pixel density 1.6X body.

To start, as was noted, you need to divide a FF pixel count by 1.6 squared to get the equivalent pixels after you crop the image down to a 1.6X sensor size. Straight up, a 5D cropped to 1.6X will compare pretty much with the 300D.

JeffreyG wrote in post #5564238
The crop benefit is real...

There is no 'crop benefit', sensor size nor cropping have nothing to do with the fact that you are comparing different size and format images at the same size. You are simply enlarging.

nadtz wrote in post #5569735
The only reason this fallacy persists is because the 2 formats use the same lenses.

To some extent, yes. More precisely it's because we have for a long time (decades) not used the angle of view of a lens to describe the angle of view, but used the focal length instead. As a certain focal length gives a certain angle of view, provided the format is the same, this was no problem back in the film days. Everyone using these kind of cameras had the same format size, 24*36 mm, so we all knew what we meant.

Had we all been used to saying "I'm changing from a 50° lens to a 20° lens, since I need a telephoto here", then we would now instead have to have lenses with different markings, for full format, 1.3 and 1.6 crop.

apersson850 wrote in post #5569800
To some extent, yes. More precisely it's because we have for a long time (decades) not used the angle of view of a lens to describe the angle of view, but used the focal length instead. As a certain focal length gives a certain angle of view, provided the format is the same, this was no problem back in the film days. Everyone using these kind of cameras had the same format size, 24*36 mm, so we all knew what we meant.

Had we all been used to saying "I'm changing from a 50° lens to a 20° lens, since I need a telephoto here", then we would now instead have to have lenses with different markings, for full format, 1.3 and 1.6 crop.

It's still better to use focal length to describe a lens because it is an intrinsic property of the lens and does not depend what you put behind it. Even when 'everyone' was using 35mm film, you could still crop a smaller angle out of the original image circle.

I'm sure I don't need to say there are countless trips around this same loop throughout this forum. If you do a search on 'crop factor' or 'reach' you'll probably get thousands of hits.

The 'reach benefit' is real (someone demonstrated it here recently) when comparing aps-c cameras with all except the new 1Ds MkIII, and even then I think the new 450D/XSi has a higher pixel density. This only stops giving you benefit when you outstrip the lens' resolving power.

nadtz wrote in post #5569735
There is no 'crop benefit', sensor size nor cropping have nothing to do with the fact that you are comparing different size and format images at the same size. You are simply enlarging.

OK, lemmie rephrase this. If you are going to shoot the longest telephoto you can afford and still be cropping down to an APS-C sized negative or smaller then you will be best served by the highest pixel density you can get.

In such a case a 40D will best a 5D for the final image, and be about equal to a 1Ds3.

And this is because in this very special case you are basically using your FF camera as a low pixel density smaller format.

You can poo-poo this all you want, but the bird shooters will attest to it.

The rest of us (that are not cropping much) are better served by FF in all respects but cost.