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 four major groups:

• With FourThirds sensor (crop factor 2.0)
• With an APS-C type sensor (crop factor 1.5 or 1.6)
• With APS-H type sensor (crop factor 1.3)
• 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 8°/mm
• 10.5mm focal length 6°/mm
• 16mm focal length 4°/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      12
Short side px   2121    2450    2739    3024
px/mm            157     181     203     232

APS-C

with 16mm short side

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

APS-H

with 19mm short side

Megapixel          8      10      16
Short side px   2336    2592    3264
px/mm            123     137     172

Full size

with 24mm short side

Megapixel          6       8      10      12      16      21      24      28      36
Short side px   2000    2309    2582    2828    3266    3742    4032    4320    4900
px/mm             83      96     108     118     136     156     168     180     204

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       7       8      10      12
APS-C      MP      -      -       6       8      10      11      12      15      20
APS-H      MP      -      -       8      10       -      16      -       -       -
Full size  MP      6      8      12      16      21      24      28      36      46
pixel/mm          80    100     120     140     160     170     180     204     230
f=5.6mm  size   2520   3150    3780    4420    5050    5360    5680    6440    7260 
f=8mm    size   3600   4500    5400    6300    7200    7600    8100    9180   10350
f=10.5mm size   4800   6000    7200    8400    9600   10200   10800   12240   13800 
f=16mm   size   7200   9000   10800   12600   14400   15300   16200   18360   20700

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

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