How can measurements be made when you can’t directly measure them?  Measuring the height of a building could be done by someone hanging a string from the rooftop and then measuring the string.  What if you can’t get access to the rooftop?  What if you needed to measure the span of a lake or height of a mountain?  Good luck using that string.  Here is how FOV can be used as a measurement tool for objects in pictures, videos, etc.  First lets define FOV.

“The field of view is the extent of the observable world that is seen at any given moment. In case of optical instruments or sensors it is a solid angle through which a detector is sensitive to electromagnetic radiation.”
-Wikipedia, https://en.wikipedia.org/wiki/Field_of_view

I want to take time to cover this topic and some measurements I’ve made of FOV.  Image sensors have a viewable work area that they can detect.  This is the FOV.  There are other sensors as well that have definable FOV ranges.  Here are examples of sensors with working FOV ranges.

Image – https://www.sparkfun.com/products/14028 or https://www.adafruit.com/products/3099
Near IR – https://www.sparkfun.com/products/11610 or https://www.adafruit.com/products/3100
Far IR (heat) – https://www.sparkfun.com/products/13233  or http://www.digikey.com/en/product-highlight/m/melexis/mlx90621-16-x-4-pixel-thermal-imager
Ultrasonic – https://www.sparkfun.com/products/11724 or https://www.adafruit.com/products/1137
LIDAR – https://www.sparkfun.com/products/14032
Distance IR – https://www.adafruit.com/products/1568

There are at least 3 classes of FOV.  These are Horizontal, Vertical, and Diagonal.  I’ll reference them as hFOV, vFOV, and dFOV respectively.  The sensors I listed above have definable FOV specs.  The spec can also define the operational range, how far away an object can be detected.  Here are some visual examples to better describe the concept of operational range.

This image has 4 objects in a black background.  The objects vary in brightness due to their distance from the sensor.  You may say you only see 3 objects.  That is because the 4th object is outside the operational range, it blends in with the background.  The sensor can not see it and as a result, neither can you.

This video shows three different FOV values for the same image sensor.  These are wide, medium, and narrow.  The description indicates the angular differences between them.  The wide FOV image contain more objects and spans a larger area, however the pixel resolution is lower for a given object.  In contrast, the narrow FOV image spans a smaller area but has higher resolution of specific objects.

The FOV can be calculate using two measurements, first being the distance of the sensor perpendicular to field, and the next being the width, height, or diagonal distance of the field.  Here is the formula to determine FOV angle.

hFOV = horizontal angle in degrees
w = field width distance, in inches
d = distance of sensor to plane, in inches

hFOV = arctangent ( w / d )

I’ll use an example of my 808-16 key chain camera.  It has a wide angle lens and records video with a resolution of 1280 x 720 at 30 frames per second.  It is mounted above a table at a distance of 17″.  I measured the span of its viewable range at 51″.  Here is the hFOV for that camera.

hFOV = arctangent ( 51 / 17 )
hFOV = arctangent * 3
hFOV = 112.62 Degrees

Doing some math, I can determine the pixel resolution of my 808-16 using the width 1280 and height 720 resolution values

pRES = pixel resolution in degrees
pRES = hFOV / w
pRES = 112.62 / 1280
pRES = 0.087984375 degrees

Now I can determine the vFOV by multiplying pRES by the height of 720, this give me 63.34875 degrees.  Finding the diagonal value will require finding the hypotenuse of 1280 and 720.  The hypotenuse will be 1,468.604780055

h = sq-root (1280^2 + 720^2)
h = sq-root (1638400 + 518400)
h = sq-root 2156800
h = 1468.604780055

With a diagonal pixel distance established at 1469 (rounded to the nearest whole number), we can determine the dFOV.

dFOV = 1469 * pRES
dFOV = 1469 * 0.087984375
dFOV = 129.249046875 degrees

This all may still seem abstract and the results look like they have no practical use.  However, knowing these values can be useful to determine the size of objects in photos and videos.  Fairly accurate measurements of buildings, lakes, mountains, and any other objects can be made using these values as a reference.  This is exactly how measurements are made of objects that are beyond physical reach, such as planets, stars, and galaxies.  FOV is a tool set for measurement in many areas of study.  I’ll be covering field scanning in my up coming post, this will expand on the concepts covered here.

Thank you for sticking with me through the math.

Enjoy!