### Angle of Coverage vs Image Circle

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HI,

I'm planning to acquire a LF system(possible a Horeseman 45FA) to get better nature chromes then with my 35mm. I want to use the 6 x 9 and 6 x 12 rollbacks because the 120/220 film is cheaper and the ease of use. For the 6 x 9 format, I calculate a required circle of 108.167 mm. For the 6 x 12 format, I come up with a circle of 134.164 mm. In order to calculate the angle of view for a given lens, I just form a simple ratio of the image circle required for the given format.

As a example, for the Nikkor W 105/f5.6 LF lens, we have an angle of coverage of 73 degrees at an image circle of 155 mm. Then for the 6 x 9 format we calculate an AOV(angle of view) of 73*108.167/155 = 50.94 deg. For the 6 x 12 format, the AOV = 73*134.164/155 = 63.187 degrees. Since the image angle is realy calculated from the horizontal distance, the true angle of coverage for these two examples will be slightly less then as calculated.

Question. Is this logic correct?

Question. Would a Nikkor SW 90/f8(IC=231mm, AOC=105 deg.) be a better LF lens to start off with? For this I calculate AOV(6x9) = 105* 108.167/231 = 49.167 degs and AOV(6x12) = 105*134.164/231 = 61 degs.

Question. Is the F8 lens to slow and does it need a center filter?

John

-- John C. Potter (potter@cubic.com), November 30, 1998

I'm afraid the logic is incorrect. The formula for the diagonal angle of view is

A = 2 arctan(D/(2F))

where D = diagonal length (for the format in question) and F = focal length of the lens. Here arctan is the same as tan^(-1) or inverse tangent and is measured in degrees, not radians. (If your calculator gives radians, convert by multiplying by 360/(2 pi), with pi = 3.14159265.)

Example. Take F = 105mm, as in your example. The 6 x 9 format measures 56 x 84mm (not 60 x 90mm!). So take D = 100.96mm in the formula. We get D/(2F) = 0.48074, so A = 0.89624 radians, or A = 51.35 degrees. Coincidentally, this is close to your answer. If F = 90mm, we find A = 58.57 degrees.

If you really want the horizontal angle of view, replace D in the formula by H, the horizontal length of the format. You'll get A = 43.60 degrees when F = 105mm, and A = 50.03 degrees when F = 90mm.

I believe (but am not 100% certain) that the 6 x 12 format measures 56 x 112mm, so you can easily redo the calculations in this case if desired. I hope this helps.

-- Stewart Ethier (ethier@math.utah.edu), November 30, 1998.

Forget the calculations, IMHO they are unnecessary. What you want to know is will this lens cover my format? and, How much shift will I have with this lens? For the answer to both of those you need to know what the diameter of the image circle is at f/16 or f/22 when focused at infinity (or a distance that approximates it; image circle becomes larger as you focus closer since the lens is farther from the film than when focusing on far distances.) View Camera magazine earlier this year published a table giving the 35mm approximations for several formats and focal lengths. it would be nice if they updated their website to include this table or allowed Quan to publish it in the static content at this web site.

-- Ellis (evphoto@insync.net), December 01, 1998.

John, The previous posters have already dealt with the HARD stuff! So.....

The Nikkor SW 90mm f/8 would be an excellent choice for both the 6x9 and 6x12 roll film formats. It would be a better choice than the 105mm W 5.6, particularly with the 6x12 format.

The 90mm SW f/8 has a much larger image circle (235mm at f/16) than the 105mm W 5.6. While the 105mm W will be fine for 6x9, it may not provide enough coverage for 6x12. And if and when you decide to use 4x5 film in the future, the 90mm SW will provide more than ample coverage and movements.

On the 6x9 roll film format, the 90mm SW will be equivalent to a 35mm focal length on the 35mm format. The 90mm SW on the 6x12 or 4x5 format would be equivalent to about a 24-28mm focal length on the 35mm format.

F/8 is not too slow for a LF lens. I don't think you'll ever actually make an exposure at maximum aperture in LF; a taking aperture of f/16 or f/22 will be more likely.

A large maximum aperture would only be important when composing and focusing on your groundglass in low or dim light situations. A 90mm f/8 WA will be a little less bright on the groundglass when composing and focusing, but not noticeably less so than a 5.6 lens. (Nikkor has a f/4.5 90mm SW if you're concerned about this, but it costs nearly twice as much as the f/8 version).

Lastly, you will not need a center filter for 6x9, 6x12, or 4x5 with the 90mm SW. You may need one with the 105mm W on the 6x12 format, though.

Good luck, Sergio.

-- Sergio Ortega (s.ortega@worldnet.att.net), December 01, 1998.

Thanks for the info! Its looks like a Nikkor SW 90/f8 would be a good lens to start for 6 x 9 and 6 x 12 formats including 4 x 5. The test results for this lens looks superior.

-- John Potter (potter@cubic.com), December 01, 1998.