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# Matching AoV w/ alternate lens & sensor size

> a = 2 \* arctan(.5 \* F / f)

Where **a** is the *Angle Of View*, **F** is the *film-back size* and **f** is the *focal length* (with **F** and **f** in the same units).

So, (for example) an 18mm lens on a super-35mm-size film-back (which is 24.0mm across the gate) has an Angle Of View of 67.4º. To get that same 67.4º Angle Of View on an IMAX 15-perf 65mm camera (with a 69.6mm film-back), you’d need a 52.2mm lens.

They haven’t made a 52.2mm lens for IMAX, but luckily they have made a 50mm. And since we’re talking about re-drawing frame lines to change the film-back size, let’s just redraw the IMAX frame lines a little: from 69.6mm to 66.7mm, because we can do the same math the other way round and find that a 66.7mm film back is the size for which a 50mm lens yields our 67.4º Angle Of View.

## F-Stop is not absolute aperture

F-Stop is proportional aperture by factor of magnification (focal length)

Reducing film-back size reduces magnification.

Smaller back size requires less magnification for same AoV. So wider lens ?

We’re scaling the magnification proportionally with the sensor

The change in Blur Circle diameter is proportional to the change in sensor size. Provided we use a lens with the same AoV.

**In order to match *Blur Circles* we need to change the diameter of the aperture proportionally with the change in magnification**

F/11
IQ-100: 53.70mm
Canon: 36mm
X100T: 23.6mm

X100T Lens: 23mm

23.6mm Across the Gate

2 \* arctan(.5 \* 23.6 / 23)

54 Angle of View

1.025

f/11 \* 36 / 53.70

To match a larger extraction

AoV = 2 \* arctan(.5 \* F / f)

Work out brackets, then the value\[tan-1] then \* 2

AoV for an 80mm lens on IQ-100 with 53.70mm across the gate

37 degree AoV – 80mm w/ IQ-100

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– Angle of View calculations are dependent on sensor AREA.
– We calculate for either width or height for ease
– We could calculate for horizontal for ‘average’
– Average isn’t best. We typically want to match horizontal angle of view or vertical, better to adjust the calculation based on attempting match angle. Vertical or Horizontal

2 \* arctan(.5 \* Sensor Length\[^Vertical or Horizontal] / Focal Length)

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Checkerboard shot for lens profile?