Appendix: Special Topics-FOV
This page offers more detail on several home theater design topics summarized in the previous theater build pages. Topics on this page include more information on the definition and estimation of the Minimum and Maximum Field of View. I worked through each of these topics myself with some help from the internet. If you find any mistakes, let me know by sending a comment.
Estimating the Field of View
Last Updated: 09/19/2024
The Field of View (FOV) calculation is straightforward but requires a little high-school trigonometry. Looking at Figure 1, we can treat the distance to the screen and half the screen's width as two sides of a right triangle. Using the arc tangent function, we can take the two sides and determine the angle from the center of the screen to the edge of the screen. The FOV is then twice this angle, as shown in the last equation.
Using the example distances of 12 ft. (144 in.) and half the screen width of 48", one can calculate the FOV using twice the arc tangent, 36.8 degrees.
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Two organizations are typically sighted (by various websites) when looking for recommended field-of-view guidelines.
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SMPTE recommends a minimum FOV of 30 degrees for movie theaters.
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THX recommends an optimum FOV of 36 degrees for a movie theater (2.35:1) and a minimum viewing angle of 40 degrees for a 16:9 screen.
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Note: There are variations in the information published by various individuals. Some of the information posted is very old. Figure 2 seems to be a good summary (see here for the original) but has not been confirmed (by the author) with the original specifications. (The author does not want to pay for the SMPTE EG 18, Design of Effective Cine Theaters.)
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Figure 1. FOV Equations
Figure 2. SMPTE/THX Theater FOV Recommendations (hopefully)
How Close is too Close to the Screen?
Last Updated: 09/02/2024
How close one sits to the screen can be a personal preference and depends on several factors.
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Sitting so close, one uncomfortably moves eyes around the screen too much to see the whole image.
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Sitting so close that one can start to see the individual pixels.​
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The first is a personal preference, which seems to be partially accounted for in the THX and SMPTE recommendations. The second is due to the human eye's resolution, discussed below.
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Minimum (separable) resolvable acuity—A person of regular sight, measured as 20/20 vision, can differentiate two objects that cast a visual angle of 1 minute (60 seconds or 0.017 degrees). (see Evaluation of Visual Acuity)
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If one is sitting 12 feet from a 115-inch HD projector/screen (which has 1920 horizontal pixels), the field of view (FOV) is ~36.8 degrees. The angle of a single pixel is 0.019. Thus, individual pixels will likely not be detectable unless one has excellent eyesight, in which case pixels may be barely detectable. The equation used here is:
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The pixel angle of a UHD projector/screen with a horizontal resolution of 3840 will be half. Even at a six-foot seating distance, a 4K 115" screen will have a pixel angle of ~0.017.
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Figure 3. Your too close when you can see individual pixels