Testing the Lens for "The Munns Report"

Testing the PGF Lens for "The Munns Report"

So what angles and distances are required to bring Patty's height to 74" (6' 2") and 86" (7.2") and what is the optimal focal length for a solution?

I developed a computer algorithm that tests a range of parameters required to derive these standing heights. All combinations of variables that result in either standing height (e.g. 74" or 86") are listed for the following lenses: 22.5mm, 25mm, 27.5mm, 13.5mm, 15mm, 17.5mm. Since the manufacturer's specifications indicate a lens' effective focal length can vary by as much as 10%, I have assumed that a 25mm lens could have an effective focal length of +/- 10%, or +/- 2.5mm for a 25mm lens and +/- 1.5mm for a 15mm lens.

The following represents the range of test values applied to the algorithm. I have edited the output to include only the best candidate triangles for each lens type.

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Assumptions: refer to the triangle formed by vectors a (trackway), b (F480 to camera), c (F288 to camera) and angles A, B, C

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Notes:

The derivations are highly sensitive to changes in the values of "p" (image size ratio) and less so for "a" (trackway distance). The estimated angle for Patty's trackway relative to the camera, for frame 288 is approx. 130 +/- 10 degrees (40 deg from profile). This estimate is based on Patty's apparent body angle for this frame. Derived values will be compared to this angle.

Standing height estimates are based on the % of Patty's image height for a full frame (frames 288 & 480). Her image height (walking) for frame 288 was found to be approx. 170 pixels on a full frame digital scan, with the image dimensions = 1301 x 961 pixels. The typical difference in walking vs. standing height for a human ranges from 7-9% (lowest point in the stride). This is a conservative estimate for Patty. However, this will give us a lower height estimate. Therefore, Patty's standing height was estimated to be 170 + 9% = *187 pixels.

* Since applying this algorithm, I have revised my estimation of the maximum difference between Patty's walking/standing height from 9% to 18% (lowest point in the stride). This could effectively add approx. 0.25mm of focal length derived from the "best fit" estimate of the triangle. It could also add 2-3" to her standing height (which is synonymous with her body length).

The % of a full frame is then 187 / 961 = 19.5%.

Roughly: 1 foot difference in the distance from the camera = 1.2" difference in Patty's height.

Patty's size ratio "p", only affects the lengths of vectors b & c (distances from the camera to F288 & F480). It does not affect the shape of the triangle.

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The following is the output from a computer algorithm that tests a range of parameters, to derive a predefined standing height.

Range of values tested:
a = [55, 60] feet
B = [90, 180] degrees
p = [.65, .71] c/b

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To achieve a standing height of 6' 2"
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<<<<<<<<<<<<< 25mm lens >>>>>>>>>>>>>

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HAV(F288-F480)=18.65
VAV=17.3
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#	B (deg)	p [288-480]	a (ft)	Dist [288] (ft)	Hgt (in)
1	126.6	.71	58.5	104.3	73.5
2	126.6	.71	59.0	105.2	74.2
3	126.6	.71	59.3	105.6	74.5

Summary:

Angle B falls within a range of 130 +/- 10 deg.
p (.71) is likely too large to fit the model (measured=.685)

<<<<<<<<<<<< 22.5mm lens >>>>>>>>>>>>

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HAV(F288-F480)=20.65
VAV=19.17
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#	B deg	p (288-480)	a (ft)	Dist (288) (ft)	Hgt (in)
1	122.6	.71	55.5	94.1	73.5
2	122.6	.71	56.0	94.9	74.2
3	123.8	.71	57.0	94.1	73.5
4	124.9	.70	58.8	94.3	73.7
5	124.9	.69	59.3	95.1	74.3

Summary:

Angle B falls within a range of 130 +/- 10 deg.
p (.69) is a good fit for the model (measured=.685)
a=59 implies Patty's avg step length was 42"
22.5 mm lens appears to be the best fit

<<<<<<<<<<<< 27.5mm lens >>>>>>>>>>>>

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HAV(F288-F480)=16.988
VAV=15.73
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=====================
None qualified
=====================

<<<<<<<<<<<<< 15mm lens >>>>>>>>>>>>>

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HAV(F288-F480)=30.352
VAV=28.43
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=====================
None qualified
=====================

<<<<<<<<<<<< 16.5mm lens >>>>>>>>>>>>

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HAV(F288-F480)=27.771
VAV=25.94
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#	B (deg)	p [288-480]	a (ft)	Dist [288] (ft)	Hgt (in)
1	115.8	.66	55.0	70.2	74.2
2	116.8	.65	56.0	69.8	73.8
3	116.8	.65	56.5	70.4	74.5

Summary:

Angle B falls outside the range of 130 +/- 10 deg.
p (.66) does not fit the model (measured=.685 +/- .02)
a=56.5 fits Patty's avg step length of 41" (straight line)
16.5 mm lens appears to be a better fit than 15mm (but still not a good fit)

<<<<<<<<<<<< 13.5mm lens >>>>>>>>>>>>

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HAV(F288-F480)=33.447
VAV=31.44
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=====================
None qualified
=====================

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To achieve a standing height of 7' 2"
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None qualified for a 25mm lens +/- 10%
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<<<<<<<<<<<<< 15mm lens >>>>>>>>>>>>>

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HAV(F288-F480)=30.352
VAV=28.43
-----------------------------------

#	B (deg)	p [288-480]	a (ft)	Dist [288] (ft)	Hgt (in)
1	106.8	.71	55.0	74.0	85.8
2	107.9	.70	56.0	73.8	85.6
3	108.9	.69	57.5	74.3	86.1
4	109.9	.68	58.5	74.0	85.8

Summary:

Angle B falls well outside the range of 130 +/- 10 deg.
p (.69) fits the model well (measured=.685 +/- .02)
a=[56, 58.5] fits Patty's avg step length of 41" (straight line)
15 mm lens does not fit the trackway angle

<<<<<<<<<<<< 13.5mm lens >>>>>>>>>>>>

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HAV(F288-F480)=33.447
VAV=31.44
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#	B deg	p (288-480)	a (ft)	Dist (288) (ft)	Hgt (in)
1	104.7	.69	55.3	66.9	85.8
2	105.7	.68	56.3	66.8	85.7
3	106.6	.67	57.3	66.7	85.5
4	107.6	.66	58.5	66.8	85.7
5	107.6	.66	59.0	67.4	86.4

Summary:

Angle B falls well outside the range of 130 +/- 10 deg.
p (.68-.69) fits 2 estimates to the model well (measured=.685 +/- .02)
a=[55.25, 59] which fits Patty's avg step length of 41-42" (straight line)
13.5 mm lens is a worse fit than 15mm, both do not fit the trackway angle

<<<<<<<<<<<< 16.5mm lens >>>>>>>>>>>>

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HAV(F288-F480)=27.771
VAV=25.94
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#	B deg	p (288-480)	a (ft)	Dist (288) (ft)	Hgt (in)
1	110.6	.71	56.8	81.0	85.6
2	110.6	.71	57.0	81.3	86.0
3	111.6	.70	58.0	81.0	85.7
4	112.7	.69	59.5	81.3	86.0

Summary:

Angle B falls outside the range of 130 +/- 10 deg.
p (.69) fits 1 estimate to the model well (measured=.685 +/- .02)
a=[56.75, 59.5] fits Patty's avg step length of 41-42" (straight line)
16.5 mm lens is better fit than 15mm, but both do not fit the trackway angle

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Conclusions:

None of the scenarios for the 13.5, 15 & 17.5 mm lenses matched the angle of the trackway as estimated by Patty's body orientation in frames 288 & 480. This in effect eliminates the possibility that a 15mm lens +/- 10% was used to film the PGF.

The best-fit scenario was achieved with a 22.5mm lens. Here is the corresponding triangle:

Since I believe Patty's image height (pixels) was originally underestimated, the standing height for the above scenario should be revised to 6' 3", and the optimal focal length to 23mm.