# DSLR spherical resolution

## Intro

In general photography megapixels are more or less synonymous to resulting image resolution. Panorama photography is a bit different, especially spherical panoramas. Here the sensor pixel density is more important than the sensor pixel count.

## The Problem

Digital Single Lens Reflex (DSLR) cameras exist in three major groups:

• With FourThirds sensor (crop factor 2.0)
• With an APS-C type sensor (crop factor 1.5 or 1.6)
• With a sensor of the full 35mm film size (crop factor 1.0)

In each size category there are several cameras with different sensor resolutions. And there are several lenses that can be attached to cameras with different sensor sizes. To have the effects of different lenses comparable the concept of a 35mm equivalent focal length has been established - the real focal length multiplied with the crop factor gives the same Field of View like for a 35mm film camera.

However, this is not possible for fisheye lenses, since the Focal Length does not correspond linearly to the Field of View. One has to look at the degree/mm ratio and absolute pixel density instead.

## Degree/mm

In the Fisheye Projection an angular distance from the optical axis maps to a linear distance on the sensor. The mapping is determined by the focal length (the following numbers are approximations, since real fisheyes almost never resemble the ideal fisheye mapping):

• 5.6mm focal length 11.4°/mm
• 8mm focal length 7.2°/mm
• 10.5mm focal length 5.5°/mm
• 16mm focal lenght 3.6°/mm

## Pixel density

To deduce the pixel resolution obtainable by a certain sensor/lens combination we should know the density in pixels/mm of the respective sensor. The pixel density can be calculated roughly from the Megapixels (better would be actual pixel size) and the sensor size. For the three major groups and some typical Megapixel sizes:

FourThirds with 13.5mm short side

Megapixel       6       8       10
Short side px   2121    2450    2739
px/mm           157     181     203


APS-C with 16mm short side

Megapixel       6      8       10      12
Short side px   2000   2309    2582    2828
px/mm           125    144     161     177


Full size with 24mm short side

Megapixel       6       8       10      12      16      21
Short side px   2000    2309    2582    2828    3266    3742
px/mm           83      96      108     118     136     156


## Pano sizes

From the above values we can easily calculate some sample panorama resolutions. The table gives some rounded values for the maximum pixel size of an equirectangular:

FourThirds MP   -       -       -       -       6       8       10
APS-C      MP   -       -       6       8       10      12      -
Full size  MP   6       8       12      16      21      -       -
pixel/mm        80      100     120     140     160     180     200
f=8mm    size   4000    5000    6000    7000    8000    9000    10000
f=10.5mm size   5200    6500    7900    9200    10500   11800   13100
f=16mm   size   8000    10000   12000   14000   16000   18000   20000


The formula for an exact calculation is ${\frac {pixel/mm}{degree/mm}}*360$

--Erik Krause 22:11, 21 August 2007 (CEST)