DSLR spherical resolution

Intro

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

Cameras

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.

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 and the sensor size.

You get the exact pixel density by dividing the sensor size in pixels by the corresponding size in mm.

For the four major groups and some typical Megapixel sizes:

FourThirds

with 13.5mm short side

Megapixel          6       8      10      12      16      20
Short side px   2121    2450    2739    3024    3460    3900
px/mm            157     181     203     232     260     290

APS-C

with 16mm short side

Megapixel          6      8      10      12     15      20      24      28
Short side px   2000   2309    2582    2828   3160    3650    4000    4320
px/mm            125    144     161     177    197     228     250     273

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      42      46
Short side px   2000    2309    2582    2828    3266    3742    4032    4320    4900    5300    5500
px/mm             83      96     108     118     136     156     168     180     204     220     229

Lenses

To determine the angular resolution we need the ratio between the angular distance as seen by the camera and the physical distance on the sensor. This ratio depends on the angular distance $\theta$ from the optical axis for all projections but the equidistant fisheye. Luckily at the optical axis $(\theta =0)$ all projection formulas converge to the equidistant projection $R=f\cdot \theta$ The angle $\theta$ is expressed in radians, which gives an angular mapping of $\textstyle {\Delta R \over \Delta \theta }=f$

In simple words: The angular mapping in mm/radians equals the focal length in mm in the image center. The actual mapping is not relevant, the formula applies equally to all kinds of fisheyes as well as to normal (rectilinear) lenses.

Pano sizes

From the above values we can easily calculate some sample panorama resolutions. The table gives some rounded values for the maximum pixel width of an equirectangular (f = focal length, MP = Megapixel):

FourThirds MP      -      -       -       -       6       7       8      10      12       -      16      20
APS-C      MP      -      -       6       8      10      11      12      15      20       -      24      28
APS-H      MP      -      -       8      10       -      16      -       -       -        -       -       -
Full size  MP      6      8      12      16      21      24      28      36      42      46       -       -
pixel/mm          80    100     120     140     160     170     180     200     220     230     260     280
f=5.6mm  width  2820   3520    4220    4920    5280    5980    6340    7040    7740    8100    9140    9860
f=8mm    width  4020   5020    6040    7040    7540    8540    9040   10100   11100   11600   13100   14100
f=10.5mm width  5280   6600    7920    9240    9900   11200   11900   13200   14500   15200   17200   18500
f=12mm   width  6040   7540    9040   10560   11300   12800   13600   15100   16600   17300   19600   21100
f=16mm   width  8040  10060   12100   14100   15100   17100   18100   20100   22100   23100   26100   28100

The formula for an exact calculation is ${\text{width}}={{\text{px}}/{\text{mm}}}\cdot {\text{f}}\cdot 2\pi$

with ${\text{f}}$ = focal length, ${\text{px}}/{\text{mm}}$ = pixel density, $2\pi$ = full circle. This is the exact same formula that f.e. PTGui uses.