Dome Port Focus & Virtual Image Calculator
Enter the geometry of a dome port and your lens’s minimum focus distance to check whether the lens should focus on the distant-subject virtual image. The calculation uses a thick-wall, paraxial model rather than the usual 4r shortcut.
Required lens focus distance (mm)438.75
- Virtual image distance from center of curvature (mm)
- 388.75
- Virtual image distance in front of dome (mm)
- 282.75
- Lens focus result
- The lens should reach focus at the stated minimum focus distance.
- Focus-distance margin (mm)
- 158.75
- Equivalent close-up power (diopters)
- 2.57
- Thin-dome comparison (mm)
- 395.34
Assumes a distant subject, concentric spherical surfaces, uniform wall thickness, and the entrance pupil at the dome’s centre of curvature.
Use the dome’s inner sphere radius, not its advertised width or rim diameter.
How to use this calculator
- Enter the inner radius of the sphere that forms the dome, not the width printed on the port.
- Enter central wall thickness and choose the port material and water type.
- Estimate the distance from the entrance pupil at the dome centre back to the sensor plane.
- Enter the lens’s published minimum focus distance, measured from the sensor plane.
- Compare the required focus distance and focus-distance margin with your lens specification.
How a dome port creates a virtual image
Water, port material, and the air inside the housing bend off-axis rays. For a distant subject, those rays leave a properly centered dome as though they came from a closer point in front of it: the virtual image. The lens must focus on that virtual image, not at the real subject distance. A lens that cannot focus close enough may need a different dome, a close-up lens, or a different lens-and-housing arrangement.
This calculator uses David W. Knight’s paraxial thick-wall expression. With inner radius r, wall thickness t, air index na = 1.0003, water index nw, and port-material index np, the virtual-image distance from the centre of curvature is:
s = r / [1 − (na / nw) × {1 + (nw / np)(t / r)} / (1 + t / r)]
The distance ahead of the outer dome surface is d = s − (r + t). If b is the entrance-pupil-to-sensor distance, the focus distance the lens must reach is q = s + b. The reported margin is q − m, where m is the lens’s published minimum focus distance. A zero margin passes the simplified test exactly; a negative margin means the virtual image is closer than the lens can reach.
Thin domes, thick domes, and close-up power
For a zero-thickness dome, the expression reduces exactly to s = r / (1 − na / nw). In water this is close to the familiar 4r rule, but a real acrylic or glass dome moves the virtual image somewhat closer. The tool shows both values so the wall effect is visible. It also reports P = 1 / s(m) diopters, the approximate correction that would make rays from this virtual image parallel when the correction is at the dome centre. Treat that number as a setup clue, not a prescription for an accessory lens.
Geometry matters more than the name on the dome
Many ports sold as six-inch or eight-inch domes are not hemispheres cut from spheres of that diameter. The advertised width can describe the widest opening rather than the sphere diameter. Use the maker’s drawing, measure the curvature if practical, or ask the housing maker for the inner sphere radius. The optical centre is the dome’s centre of curvature, and the relevant lens point is the entrance pupil, not the front element, nodal point, or mount flange.
What this model leaves out
This is a distant-subject, centred paraxial estimate. It assumes concentric spherical surfaces, uniform wall thickness, and an entrance pupil located at the dome’s centre of curvature. It does not model finite subject distance, off-axis field curvature, spherical or chromatic aberration, pressure deformation, manufacturing tolerance, water temperature, or wavelength. A lens that passes this centre-focus check can still show soft corners, so confirm port extension, aperture, and focusing behaviour in a controlled in-water test.
Worked example
Consider a 100 mm inner-radius acrylic dome with a 6 mm central wall in seawater. The thick-wall denominator is 1 − (1.0003 / 1.339) × {1 + (1.339 / 1.490) × 0.06} / 1.06, or about 0.2572353. The virtual image is therefore 388.75 mm from the centre of curvature and 282.75 mm in front of the 106 mm outer radius.
With a 50 mm entrance-pupil-to-sensor distance, the lens must focus at 438.75 mm from the sensor. A lens whose published minimum focus distance is 280 mm has a 158.75 mm positive margin, so it passes this simplified test. The corresponding thin-dome result is 395.34 mm, and the approximate infinity correction is 2.57 diopters.
Common questions
Why does a dome port create a virtual image?
A dome separates water, port material, and the air in the housing, so off-axis light changes direction at the curved surfaces. The refracted rays reaching the lens appear to originate from a point much closer than the distant subject. The camera therefore focuses on that apparent, or virtual, image.
Is dome diameter the same as sphere diameter?
Not necessarily. The advertised size of a commercial port often describes its rim or widest physical width, while its curved surface can be part of a larger sphere. This formula needs the inner sphere radius, which is half the sphere diameter, rather than the advertised port width.
Where is a lens minimum focus distance measured from?
Camera and lens makers normally measure minimum focus distance from the sensor or film plane, often marked on the camera body. It is not the clearance between the front of the lens and the subject. Use that manufacturer specification here, then add the entrance-pupil-to-sensor distance as the model requires.
Why must the entrance pupil align with the dome centre of curvature?
When the entrance pupil is at the centre of curvature, rays aimed through it meet the spherical surfaces near normal incidence. That arrangement helps preserve field of view and is the alignment assumed by the model. Moving the pupil away introduces errors that this centre-axis focus calculation does not quantify.
When does an underwater lens need a close-up diopter?
A close-up lens can help when the dome’s virtual image falls closer than the lens can focus. The reported diopter figure is an approximate infinity correction based on the virtual-image distance, not a guarantee of which accessory will work. Lens design, diopter placement, port geometry, and corner performance still need a real in-water test.
Why do thick acrylic and glass domes differ from the 4r rule?
The 4r rule treats the dome as an infinitely thin water-to-air boundary. Real ports have thickness and a material refractive index, so light refracts at two separated curved surfaces. The thick-wall formula accounts for those terms and normally places the virtual image closer than the thin-dome estimate.