TITLE: I made a mistake with cropping fisheye photos to a field of view
DATE: 2018-10-10
AUTHOR: John L. Godlee
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In a previous post I created an R function to estimate the radius in
pixels of a circle with a view angle of given degrees, for a fisheye
lens with an equisolid project. I realised afterwards, after doing
some testing that this function didn’t work. It was close, but some
things didn’t work quite right. For instance when I changed the
focal length of the lens, nothing in the output of the function
changed. Here is the new function, which uses the pixel pitch of the
camera sensor:

   fov.px <- function(deg_theta, focal_length_mm, pixel_pitch_um){
       require(NISTunits)

       # Convert degrees of theta to radians
       rads_theta <- NISTdegTOradian(deg_theta)

       # Calculate radius of circle drawn by angle of view (rads_theta and max_rads_theta) in mm projected onto the sensor plane
       R <-  2 * focal_length_mm * sin(rads_theta / 2)

       # Calculate the px per mm on the sensor, i.e. the pixel pitch
       sensor_px_per_mm_flat <- 1/pixel_pitch_um * 1000

       # Multiply the mm radius of the desired circle by the number of pixels per mm on the sensor, to get the number of pixels radius of the desired circle
       pixels_for_theta <- R * sensor_px_per_mm_flat

       # Print result
       print(paste("Radius of circle:", round(pixels_for_theta, digits = 0), "px"))
   }

-   deg_theta = the desired radius to be cropped to, in degrees.
   e.g. a full 180deg fov = 90
-   focal_length_mm = focal length of the camera lens combo, e.g. 8
-   pixel_pitch_um = the pixel pitch, i.e. the number of micrometres
   per px, e.g. 5.95

Similarly, I made a function which can calculate the theta (degrees
of radius) of a circle of a given proportional circular crop of the
original circle:

   fov.theta <- function(prop_crop, full_circle_radius_px, focal_length_mm, pixel_pitch_um){
       require(NISTunits)

       # Calculate the number of pixels in the radius of the crop
       px_crop <- full_circle_radius_px * prop_crop

       # Calculate the radius of the
       theta <- 2 * asin(((pixel_pitch_um * px_crop) / (2 * focal_length_mm * 1000)))

       deg_theta <- NISTradianTOdeg(theta)

       print(paste("Angle of view: ", round(deg_theta, digits = 2), "°", sep = ""))
   }

-   prop_crop = proportion of the projected circular image radius
   that has been cropped, e.g. 0.59
-   full_circle_radius_px = Radius of the full uncropped circle in
   pixels, e.g. 1962
-   focal_length_mm = focal length of the camera lens combo, e.g. 8
-   pixel_pitch_um = the pixel pitch, i.e. the number of micrometres
   per px, e.g. 5.95