# User:The Lamb of God/sandbox

The Field of View of an imaging sensor or imaging system is defined as the maximum vertical and horizontal angular extent "viewed" by the sensor or system. Optical tests for measuring the FOV are versatile tests capable of measuring the FOV of UV, visible, and infrared sensors; (about .1-20 microns in the electromagnetic spectrum).

## Field of view test

The Purpose of this test is to calculate the horizontal and vertical Field of View of a lens used in an imaging system or sensor.

Schematic of optics apparatus used in testing the FOV of a camera.

## Optical apparatus

UV/Visible light from an Integrating sphere is combined with infrared radiation from a BlackBody and is focused onto the focal plane of a collimator. A square test target lays in the focal plane of the collimator. Within the collimator, the light from the square test target is reflected off of a fold mirror, (flat plane mirror), unto an off-axis parabolic mirror. The incident light/radiation to the parabollic mirror is reflected/collimated back through the other end of the collimator. This means that all the light reflecting off the off-axis parabolic mirror is now near perfectly parallel. The Unit Under Test processes the collimated light/radiation and the image is displayed on a monitor. [1]

File:FOV Target on Monitor.jpg
Monitor Display of Camera (Unit Under Test)

## Monitor display

The target is displayed on a monitor in pixels. Dimensions of the screen display in pixels are known and the dimensions of the displayed target are determined by inspection.

• $D_y\,\!$ = Vertical Dimension of Display (pixels)
• $D_x\,\!$ = Horizontal Dimension of Display (pixels)
• $d_y\,\!$ = Vertical Dimension of Image of Target (pixels)
• $d_x\,\!$ = Horizontal Dimension of Image of Target (pixels)

## Angular extent

To Calculate angular extent of the target $(\alpha\,)$ use the following formulas...[2]

• $\alpha\,_x = 2 \arctan (\frac{L_x}{2f_c})$

• $\alpha\,_y = 2 \arctan (\frac{L_y}{2f_c})$
• $L_x\,\!$ = Horizontal Dimension of Target
• $L_y\,\!$ = Vertical Dimension of Target
• $f_c\,\!$ = Focal Length of Collimator

For a derivation of the angle of extent formula see "Derivation of the angle-of-view formula" under the article Angle of view

### Example Calculation

• Dimensions of square target and focal length of the collimator are initialy known.
• Given: $f_c\,\!$ = 2000.00mm, $L_y\,\!$ = 25.00mm, and $L_x\,\!$ = 25.00mm
• Find: horizontal and vertical angular extent $\alpha\,_x$ and $\alpha\,_y$ in radians (rad).
• Solution:
• $\alpha\,_x = 2 \arctan (\frac{25mm}{2*2000mm})$
• $\alpha\,_x = .0125 rad$
• $\alpha\,_y = .0125 rad$

## Calculating the field of view

The Horizontal and Vertical fields of view ($HFOV\,$ and $VFOV\,$, respectively) are estimated (in radians) from the value of angular extent (in radians) multiplied by the display pixel count divided by the target pixel count.[3]

• $HFOV = \alpha\,_x \frac{D_x}{d_x}$

• $VFOV = \alpha\,_y \frac{D_y}{d_y}$

### Example Calculation

• Dimensions of screen display are initialy known and dimensions of target are known from inspection.
• Given: $D_x\,\!$ = 1280pixels, $d_x\,\!$ = 640pixels, $D_y\,\!$ = 1024pixels, $d_y\,\!$ = 640pixels, and $\alpha\,_x$,$\alpha\,_y$ = .0125rad
• Find: horizontal and vertical field of view ($HFOV\,$ and $VFOV\,$) in radians (rad).
• Solution:
• $HFOV = \alpha\,_x \frac{1280px}{640px}$
• $VFOV = \alpha\,_y \frac{1024px}{640px}$
• $HFOV = .025rad\,$
• $VFOV = .0120rad\,$

## References

1. ^ Mazzetta, J.A.; Scopatz, S.D. (2007). Automated Testing of Ultraviolet, Visible, and Infrared Sensors Using Shared Optics. Infrared Imaging Systems: Design Analysis, Modeling, and Testing XVIII,Vol. 6543, pp. 654313-1 654313-14
2. ^ Young, H.D., Freedman, R.A. (2004). University Physics (11th ed.).San Fransisco, CA: Addison Wesley
3. ^ Electro Optical Industries, Inc.(2005). EO TestLab Methadology. In Education/Ref. http://www.electro-optical.com/html/toplevel/educationref.asp.