I fail to understand why the field of view of a particular lens is "photography," but not math. Aside from the approximations made about the model of a lens' geometry, it is *exactly* math that describes it's view. Artistic/photographic notions have no bearing: the angle of stuff you can see in the viewfinder is a function of what lens you put in front of the sensor. That is all.

Judging by your response, I'm not convinced I was clear enough in my description, so here goes again. From what I have read, the angle of view of a 16mm fisheye *on a 1.5 crop factor DSLR* is approximately the same as a 20mm lens *on a 35mm frame size*. Take a look here:

http://www.photo.net/learn/fisheye/

Now, with the additional distortions pincushion/barrel, each lens may see more bits in the corners or edges or enlarge the center. That means that some parts of the image may go missing when you reproject to the other's projection.

-Cory

On Sat, 23 Apr 2005, Shel Belinkoff wrote:

Too much math, not enough photography .... I don't understand the need for
equations, nor do I understand the math, the equations, or your conclusion.

Like I said, the field of view, regardless of your math, is greater with
the Zenitar than it is with a 20mm lens on a 35mm camera. Have you looked
through both focal lengths on a 35mm camera?  Have you actually compared
photos side-by-side?

Shel


[Original Message]
From: Cory Papenfuss

        Perhaps I wasn't clear enough in my post.  I scoured the 'net for
some equations on rectilinear vs. fisheye projections horizontal and
vertical FOV.  They're approximate (especially for the fisheye), but are
as follows:

Rectilinear:    FOV = 2 atan (image size/(2*focal length))
Fisheye:        FOV = 4 asin (image size/(4*focal length))

Given 35mm film size of 35.8x24.3mm, and the -DS sensor at 23.5x15.7mm,
you get these numbers (in degrees X by Y landscape mode):

20mm Rect: 83x63 (35mm), 61x43 (1.5 crop)
14mm Rect: 104x82 (35mm), 80x59 (1.5 crop)
16mm Fish: 136x89 (35mm), 86x57 (1.5 crop)

        So, what I *meant* to say is that FOV of the fisheye is about
equivalent to a 13-14mm rectilinear lens on the -DS, or a 20mm
rectilinear
lens on a full-frame 35mm body.

-Cory

  On Sat, 23 Apr 2005, Shel Belinkoff wrote:

Huh!

I've used a 16mm Zenitar, an 18mm and 20mm Pentax on a 35mm camera.  The
Zenitar isn't a 20mm ... it's CONSIDERABLY wider than the 20mm and the
18mm.  How do you arrive at the conclusion that the 16mm Zenitar
equates to
20mm coverage on 35mm?

Shel

On Sat, 23 Apr 2005 11:31:44 -0400 (EDT), Cory Papenfuss wrote:

Anyway, the 16mm Zenitar fisheye can be had for $100-$150 and
equates to about 20mm coverage on a 35mm, or 13-14mm
rectilinear on a 1.5 cropped body.




*************************************************************************
* Cory Papenfuss                                                        *
* Electrical Engineering candidate Ph.D. graduate student               *
* Virginia Polytechnic Institute and State University                   *
*************************************************************************




*************************************************************************
* Cory Papenfuss                                                        *
* Electrical Engineering candidate Ph.D. graduate student               *
* Virginia Polytechnic Institute and State University                   *
*************************************************************************



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