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