# If you cant get closer... get a cropped sensor.. magic!

Started Apr 7, 2010 | Discussions thread
Reach and its relationship to pixel density

number95 wrote:

Robsphoto wrote:

number95 wrote:

Interesting to see how a topic like this got too much attention. Almost 100 posts...Anyway, reach comparison of two cameras normalised according to same pixel density on the final image can be calculated by (MP1/MP2)^0.5 x CF2/CF1 where MP1: pixel count of camera 1, MP2: pixel count of camera 2, CF1: crop factor of camera 1, CF2: crop factor of camera 2.. For instance, if we compare 5dmkII which has 21mp and crop factor 1 with a 40D a 10mp camera with 1.6x crop factor, 5D has only approximately 10% reach disadvantage over 40d. If 18mp 7D comes into equation, 5d will have more than 30% reach disadvantage over 7D, or in other words 7d will have more than 30% reach on the final image after same pixel density adjustment.

Thanks for your interesting post. When you apply the formula you have given above, you get a comparison of the difference between the pixel density (in linear terms) of two cameras. If you apply this formula to a simple example, you can see this quite clearly. For example, assume the following:

Camera 1 has a sensor size of 22.5mm x 15mm and has 13.5 megapixels (4500 pixels x 3000 pixels). The pixel density in pixels per linear centimetre is 2000 (4500 / 2.25). The crop factor is 1.6x (36mm / 22.5mm).

Camera 2 has a sensor size of 36mm x 24mm and has 24 megapixels (6000 pixels x 4000 pixels). The pixel density in pixels per linear centimetre is 1666.67 (6000 / 3.6).

Therefore, the pixel density of Camera 1 is 20% (or 1.2x) greater than that of Camera 2 (2000 / 1666.67).

This can be confirmed by using the formula you have given above (the camera with the smaller sensor needs to be entered first).

(13.5mp / 24mp )^0.5 * (1.6 / 1.0) = 1.2

For the sake of clarity, I refer to this 20% difference in my notes as a “pixel density advantage”.

(Analysis of the 49% pixel density advantage of the Canon 7D over the Canon 5DMarkII).

I agree, whatever it is, either density or reach, it is advantage for that purpose

I shall endeavour to explain the effect of the pixel density advantage in more detail. Perhaps someone can check whether or not they agree with the conclusions shown below!

I shall use the above example, but I shall refer to Camera 1 as APS, because it is an APS-C camera, and I shall refer to Camera 2 as FF, because it is a full frame camera. You should also assume that a 300mm lens is attached to both APS and FF.

The effect of the pixel density advantage in the above example, depends on whether an image from FF is cropped to the same field of view as an image from APS, or whether it is cropped to the same image width as an image from APS.

As demonstrated above, the pixel density (in pixels per linear centimetre) of APS is 20% greater than that of FF (2000 / 1666.67).

If you crop an image from FF to the same FIELD OF VIEW (FOV) as an image from APS, the image width is 3750 pixels (6000 x 22.5 / 36.0).

The uncropped image width of APS is 4500 pixels, so when both images show the same FOV, an image from APS is 20% wider than that of FF (4500 / 3750). This is because the pixel density of APS is 20% greater than that of FF.

It depends on how you define the term “reach”, but in this example, you could say that, there is no difference in the reach when an image from FF is cropped to the same FOV as an image from APS.

This is because, the FOV of an image from APS is 480mm (300mm x crop factor of 1.6), and the FOV of a cropped image from FF is also 480mm (300mm x 6000 / 3750).

However, if you crop an image from FF to the same IMAGE WIDTH as an image from APS, then the image width of both images is 4500 pixels. In these circumstances, the FOV of an image from APS remains at 480mm (300mm x crop factor of 1.6).

But, the FOV of a cropped image from FF changes to 400mm (300mm x 6000 / 4500).

Therefore, in the above example, when an image from FF is cropped to the same image width as an image from APS, the reach of APS is 20% greater than that of FF (480mm vs 400mm). This is because the pixel density of APS is 20% greater than that of FF.

Note that a detailed explanation about the mathematical formulas, and the advantages and disadvantages of cropping images to gain extra reach, can be seen here:

http://www.robsphotography.co.nz/focal-length.html

Regards
Rob

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