[MF3D.FORUM:102] Re: Image Size

[Richard Rylander <rlrylander@xxxxxxx>]

I see as my message about image size bounced back to me that the table
got a little scrambled through font substitution.  Here it is again
in a hopefully more readable form (view this with "Fixed Width" font, size
10).

Consider a rectangle "w" units wide, "h" units high, viewed from a point
"f" ('focal length' of viewer lens) units away from the center of the
rectangle.  The "1D" angular width, "aw", and angular height, "ah", [the
easy calculations] are:

    aw = 2*arctan(w/(2f))         ah = 2*arctan(h/(2f))

The "2D" solid angle, "s" is a little trickier:

    s = 2*pi - 4*arccos(sin(aw/2)*sin(ah/2))

In the table below, "F" is the viewer focal length, "S" is the solid angle (in steradians), "Adj. S" is the adjusted solid angle ("S" divided by the square root of the format aspect ratio), and the "Immersion Factor" is the fraction of a hemisphere the adjusted solid angle represents.

Format    Size      F      S      Adj. S   Immersion Factor
5P      23 x 21    44    2.0896   1.9967        0.3178
7P      23 x 28    44    2.4174   2.1910        0.3487
MF      50 x 50    78    2.6838   2.6838        0.4271
3Disc   24 x 36    43    2.7753   2.2660        0.3606
MF-W    56 x 58    78    2.9964   2.9443        0.4686
6 x 7   60 x 70    78    3.2876   3.0437        0.4844

Does "Immersion Factor" = "WOW" ?  This seems to support the various
MF's.

Richard Rylander