A color wheel moves successive optical filters through a fixed light path. In the example here, an RGB sequence filters broadband light at one off-axis spot while a motor turns the wheel. A reference mark provides a once-per-revolution timing signal. The calculator concerns wheel and sector timing, not image quality or an entire projector design.
Color Wheel Optics Interactive Calculator
Set wheel speed and nominal sector angle to calculate revolution frequency, ideal sector dwell and physical sector-boundary rate. A shorter final sector fills the remaining angle when the nominal size does not divide 360°. The animation shows the filter under a fixed light spot, slowed for inspection.
Equation Used
- Uniform rotation and ideal beam-center timing.
- First sectors use the selected width; the final sector closes the 360° disc.
- Illustrative repeating RGB assignment; not a specific projector wheel.
- A reference mark passes the pickup once per revolution.
- Numerical times use actual rpm; visual playback is 1,200 times slower.
Generic RGB filter sequence with a shorter closing sector where needed. Actual rpm drives numerical timing; animation is slowed 1,200 times. Ideal beam-center timing only.
How the filter wheel changes color
The disc carries filter sectors around a central motor hub. Light crosses the wheel plane at a fixed point outside that hub. As each sector reaches the spot, its transmitted band enters the downstream optics. The beam crosses the wheel plane through the selected filter sector.
In the illustrated arrangement, an index mark rotates with the disc and passes a fixed pickup once per turn. The timing strip represents the filters passing the beam center during that revolution. The displayed colors identify nominal red, green and blue filters; they are not calculated spectra.
Real illumination has a finite footprint. While a sector boundary crosses that footprint, the light can contain contributions from adjacent filters. This calculator omits that transition interval and reports ideal beam-center timing. Synchronization, usable color time and optical throughput require additional system information.
Where optical filter wheels are used
Continuous filter wheels can provide sequential illumination in optical systems such as some single-imager projectors. Stepped filter wheels instead park individual filters in a beam for imaging or measurement. The calculator here assumes continuous uniform rotation, not a step-and-settle positioning sequence.
Wheel and sector timing
For N revolutions per minute and a selected sector angle θ in degrees:
T = 60,000/N milliseconds per revolution
t = T × θ/360 milliseconds per selected sector
n = ceil(360/θ)
Boundary rate = n × f
The illustration uses n physical sectors. The first n − 1 have angle θ; the final sector has angle 360 − (n − 1)θ. If θ divides 360 exactly, all sectors are equal. Otherwise the closing sector has a shorter dwell. The boundary rate is an average count of physical sector edges per second, not a claim that all intervals are equal.
A sector boundary is not necessarily a change of transmitted color: the illustrative repeating RGB assignment can put the same color on both sides of the closing edge. Neither this rate nor the revolution frequency is automatically the projector frame rate or complete RGB-cycle rate.
Worked timing examples
At 7,200 rpm the wheel turns at 120 Hz and one revolution takes 8.333 ms. A 60° sector occupies one sixth of that time: 1.389 ms. Six such sectors fill the disc, giving 720 sector-boundary passages per second.
Change the nominal angle to 73°. Four 73° sectors use 292°, leaving a fifth sector of 68°. The four full-width sectors each take 1.690 ms and the final sector takes 1.574 ms. There are five physical boundaries per revolution, so the average boundary rate is 600 per second.
What changing speed and angle does
Increasing rpm shortens every angular interval in inverse proportion. Increasing a sector’s angle gives that sector more of each revolution. The remaining angular space must still be allocated; the illustration uses a shorter final sector when necessary. No universal bit depth, motor lifetime, flicker threshold or image-quality score follows from these two inputs alone.
Color-wheel timing questions
Why is there sometimes a shorter sector?
A wheel must close at 360°. If the chosen angle does not divide 360 evenly, the final sector fills the remaining angle and has a shorter dwell time.
Why does the animation turn slowly?
It runs 1,200 times slower than the entered rotation rate so the beam, index mark and filter transitions remain visible. All numerical times use the actual entered rpm.
Is sector-boundary rate the video refresh rate?
No. It counts physical sector edges. The color arrangement, repeated sequences and controller timing determine how wheel motion relates to an image sequence.
Does the colored beam include transition mixing?
No. The animation follows the beam center with ideal boundaries. Finite beam size, mixed-color intervals and blanking or recovery strategies are outside this timing model.
References and scope
- Texas Instruments, DLP Discovery Optics 101 Application Note, section 3.1.3, page 16: segmented dichroic filters in the illumination path; finite-spot and spoke-transition considerations.
- Edmund Optics, rotating filter wheels: filter-wheel components and optical measurement applications.
The RGB order and remainder-sector layout here are illustrative. Timing equations are derived from constant angular speed; no specific commercial wheel is reproduced.
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