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PETS Lens Calculator

High-speed camera setup for a moving target: calculator, manual with equations, worked examples, and a short test.

Setup

Opens with the cannon example: a 20 mm projectile at 300 m/s, Chronos 1.4, 25 mm lens at 4.44 m.

Results

Scale s
Field of view W
Frames in view N
Target size
Motion blur
Travel per frame
Time in view
Frame interval
Rows (estimate)
Strip height

Compare lenses at this distance

LensScale (mm/px)Field of view (m)Strip height (mm)Target (px)Blur (px)Frames in viewChecks

Select a row to use that lens. Speed, exposure and frame rate are the same for every row.

Where to put the camera

LensDistance for this field of view (m)

Velocity from footage

After the shot, count how far the target moved in the recording. This uses the scale and frame rate set above.

Distance moved
Time taken
Measured velocity

Count frame intervals, not images: 11 images of the target span 10 intervals.

Manual: how to use the calculator

The calculator tells you, before the shot, whether a lens and camera position will give a usable measurement. Work through it in this order.

  1. Choose the camera. The menu fills in the four sensor values. If you edit any of them, the menu switches to Custom sensor.
  2. Set the camera distance first. Decide the closest safe standoff from the line of fire before anything else.
  3. Pick a lens. Use the lens buttons or type any focal length.
  4. Enter the target. Its expected speed and its size.
  5. Enter the camera settings. Exposure and frame rate.
  6. Read the checks. All four should show OK. A Check means the measurement may be unreliable, not that the shot is impossible.
  7. Compare lenses. If a check fails, the lens table shows which focal length passes at your distance. Click a row to select it.
  8. Find the camera position. Enter the field of view you need; the table gives the distance each lens needs.
  9. After the shot, use Velocity from footage to turn a pixel count into a speed.

The four checks

CheckPasses whenIf it fails
Target size10 px or more acrossMove closer, or use a longer lens
Motion blur3 px or lessShorten the exposure (needs more light), or move back
Frames in view20 or moreRaise the frame rate, or widen the view
ExposureShorter than the frame intervalShorten the exposure

The 10 px, 3 px and 20-frame limits are rules of thumb. Use your own standard if you have one. Target size and blur both depend on the scale in the same way, so moving closer improves one and worsens the other; only a shorter exposure improves blur alone.

Equations

Every result comes from the scale s: how many millimeters one pixel covers. Units are those shown in the calculator.

SymbolMeaningUnit
pSensor pixel sizeµm
DCamera distance to the plane of motionm
fLens focal lengthmm
Nx, NyPixels across, maximum rowspx
F, F0Frame rate, full-frame ratefps
vTarget speedm/s
dTarget sizemm
teExposureµs

1. Scale

s = p × Df  (mm per pixel)

D is measured from the lens (about the front of the camera) to the plane the target moves in. The formula is the far-object approximation; the exact form is s = p(D − f/1000)/f, in the same units (p in µm, D in m, f in mm). The difference is about f/(1000·D): 0.6% for a 25 mm lens at 4.44 m, and 5% for a 200 mm lens at 4 m.

2. Field of view

W = s × Nx1000  (m)

Mount the camera with the long side of the sensor along the line of travel; W uses the pixel count across that side (Nx).

3. Target size in pixels

nd = ds  (px)

4. Motion blur in pixels

b = v × te1000 × s  (px)

5. Frame interval and travel per frame

Δt = 1 000 000F  (µs)   Δx = 1000 × vF × s  (px)

6. Time in view and frames in view

tv = 1000 × Wv  (ms)   N = F × Wv  (frames)

7. Rows at a frame rate (estimate) and strip height

R = min(Ny, Ny × F0F)   H = R × s  (mm)

8. Camera distance or lens for a wanted field of view

D = 1000 × W × fNx × p  (m)   f = D × Nx × p1000 × W  (mm)

9. Velocity from footage

v = Δn × s / 1000k / F  (m/s)

The scale equation assumes the camera is much farther away than the focal length and square to the line of travel. Always confirm the real scale from a ruler image in the plane of motion.

Worked examples

Each example shows the hand calculation. Use the button to load the same inputs into the calculator and compare.

Example 1: checking a fragment-velocity setup

Given. A 10 mm fragment at 500 m/s. Chronos 1.4, 35 mm lens, 5 m away, exposure 5 µs, 10,000 fps. Will this give a usable measurement?

  1. Scale: s = 6.6 × 5 ÷ 35 = 0.943 mm/px
  2. Field of view: W = 0.943 × 1280 ÷ 1000 = 1.21 m
  3. Target: nd = 10 ÷ 0.943 = 10.6 px, passes (just)
  4. Blur: b = 500 × 5 ÷ (1000 × 0.943) = 2.7 px, passes
  5. Frames in view: N = 10,000 × 1.21 ÷ 500 = 24, passes
  6. Frame interval: Δt = 1,000,000 ÷ 10,000 = 100 µs; 5 µs fits, passes
  7. Strip: about 109 rows × 0.943 = 103 mm, so the fragment must stay within about ±51 mm of the center line
Answer. All four checks pass, two of them narrowly. Moving closer would not help on its own, because blur grows as fast as the target. Shorten the exposure first (3 µs gives 1.6 px), then move closer.

Example 2: fixing a setup that fails the blur check

Given. The cannon example (20 mm, 300 m/s, 10 µs, 10,000 fps) with a 50 mm lens at 4.44 m.

  1. Scale: s = 6.6 × 4.44 ÷ 50 = 0.586 mm/px
  2. Target: 20 ÷ 0.586 = 34 px, passes
  3. Blur: 300 × 10 ÷ (1000 × 0.586) = 5.1 px, fails
  4. Frames in view: W = 0.586 × 1.28 = 0.75 m; 10,000 × 0.75 ÷ 300 = 25, passes
  5. Fix A, exposure 5 µs: blur = 300 × 5 ÷ (1000 × 0.586) = 2.6 px, passes; costs half the light
  6. Fix B, distance 8.88 m: s = 6.6 × 8.88 ÷ 50 = 1.17 mm/px, blur 2.6 px, all checks pass
Answer. Use Fix B if the range has room: it adds standoff and needs no extra light. Use Fix A if the camera cannot move.

Example 3: choosing a lens for a required safe distance

Given. The camera must be at least 10 m from the line of fire and you need to see 2 m. Same 20 mm projectile at 300 m/s, 10 µs, 10,000 fps.

  1. Lens for exactly 2 m at 10 m: f = 10 × 1280 × 6.6 ÷ (1000 × 2) = 42 mm. No such lens, so test 35 mm and 50 mm.
  2. 35 mm at 10 m: s = 1.886 mm/px, W = 1.886 × 1.28 = 2.41 m, target = 10.6 px (just passes)
  3. 50 mm at 10 m: s = 1.32 mm/px, W = 1.69 m, too narrow
  4. 50 mm moved back: D = 1000 × 2 × 50 ÷ (1280 × 6.6) = 11.84 m; s = 1.56 mm/px, target 12.8 px, blur 1.9 px
Answer. The 50 mm lens at 11.84 m: exactly 2 m of view, a larger target than the 35 mm lens gives, and more standoff than required.

Example 4: measuring velocity from the footage

Given. In the cannon recording (scale 1.17 mm/px, 10,000 fps) the projectile moves 256 px over 10 frame intervals.

  1. Distance: 256 × 1.17 = 300 mm = 0.300 m
  2. Time: 10 ÷ 10,000 = 0.001 s
  3. Velocity: 0.300 ÷ 0.001 = 300 m/s
Answer. 300 m/s, matching the planned speed.

Test yourself

Eight questions. Use a Chronos 1.4 (p = 6.6 µm, Nx = 1280) unless a question says otherwise. Work them by hand, then check.

1. A 25 mm lens is 8 m from the line of flight. What is the scale?

2. What field of view does the setup in question 1 give?

3. At that scale, how large is a 30 mm projectile, and does it pass the target-size check?

4. A target moves at 400 m/s, exposure 8 µs, scale 1.6 mm/px. What is the blur?

5. At 20,000 fps, a 1.2 m field of view, and a target at 600 m/s, how many frames are in view?

6. At 25,000 fps, can you use a 50 µs exposure?

7. The camera must stand 12 m away and you need at least 3 m of view. Which lens works?

8. In a recording at 12,000 fps and 1.5 mm/px, a fragment moves 180 px in 6 frame intervals. How fast is it?

Show the answer key with solutions
  1. B, 2.11 mm/px. s = 6.6 × 8 ÷ 25 = 2.11.
  2. C, 2.70 m. W = 2.11 × 1280 ÷ 1000 = 2.70.
  3. A, 14.2 px, passes. 30 ÷ 2.11 = 14.2, which is above 10 px.
  4. D, 2.0 px. b = 400 × 8 ÷ (1000 × 1.6) = 3.2 mm ÷ 1.6 = 2.0.
  5. B, 40. N = 20,000 × 1.2 ÷ 600 = 40.
  6. C, no. Δt = 1,000,000 ÷ 25,000 = 40 µs, shorter than the 50 µs exposure.
  7. A, 25 mm. The longest lens that gives 3 m at 12 m is f = 12 × 1280 × 6.6 ÷ (1000 × 3) = 33.8 mm. A 35 mm lens gives only 2.90 m; 25 mm gives 4.06 m.
  8. C, 540 m/s. Distance = 180 × 1.5 = 270 mm = 0.27 m; time = 6 ÷ 12,000 = 0.0005 s; v = 0.27 ÷ 0.0005 = 540.

References and limits

Camera specifications (product pages checked 9 October 2026)

  • Kron Technologies, Chronos 1.4 high-speed camera: 6.6 µm pixels, 1280 × 1024 at 1,069 fps, C/CS mount, 1 µs shortest exposure, frame-rate table (1280 × 120 up to 8,986 fps; 1280 × 96 up to 11,184 fps).
  • Kron Technologies, Chronos 2.1-HD high-speed camera: 10 µm pixels, 1920 × 1080 at 1,000 fps, shortest exposure 10 µs.

Further reading (standard texts, cited from general knowledge)

  • Ray, S. F. (ed.), High Speed Photography and Photonics, Focal Press, 1997.
  • Settles, G. S., Schlieren and Shadowgraph Techniques, Springer, 2001.

Limits

  • The row count is a pixel-budget estimate. On a Chronos 1.4 at 10,000 fps it gives 109; Kron's table gives 120 rows up to 8,986 fps and 96 rows up to 11,184 fps, so expect roughly 100 to 108 rows at 10,000 fps. Check the camera's resolution menu.
  • The calculator does not check whether you have enough light for the exposure you choose. Make a test recording at the real settings.
  • All inputs are metric. The pass limits are rules of thumb, not standards.

Petr Explosives Group · Practical Explosives Training School (PETS).

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