Focus Stacking Step-Size Calculator for Photomicrography

Numerical Aperture
Step Size

When working with microscope objectives, the step size calculation for focus stacking becomes more critical due to the much higher magnification involved. Here’s how you can calculate the step size:

Determine the Numerical Aperture (NA)

The Numerical Aperture (NA) is usually marked on the microscope objective. It’s a critical factor in determining the depth of field (DoF) at high magnifications.

Calculate the Depth of Field (DoF)

The formula for Depth of Field at high magnifications is different from that used in macro photography and is generally given by:

[math]\large
DOF = \frac{λ}{NA^2}+ \frac{n*e}{NA^2}
[/math]

  • λ = wavelength of light (typically 550 nm for green light, which is often used as a standard)
  • NA = Numerical Aperture of the objective
  • n = refractive index of the medium between the lens and the specimen (1.0 for air, 1.33 for water, etc.)
  • e = thickness of the coverslip (typically 0.17 mm for standard coverslips)

Calculate the Step Size

For focus stacking, the recommended step size is usually 75% – 80% of the calculated Depth of Field to ensure overlap between slices.

[math]\large
Step\,Size = DoF*0.75
[/math]

Example Calculation

Assume the following parameters:

  • λ=550 nm (0.55 µm)
  • Numerical Aperture (NA) = 0.65
  • Refractive Index (n) = 1.0 (air)
  • Coverslip Thickness (e) = 0.17 mm

Depth of Field (DoF):

[math]\large
DOF = \frac{0.55}{0.65^2}+ \frac{1*0.17}{0.65^2}=1.70μm
[/math]

Step Size:

[math]\large
Step\,Size=1.7*0.75=1.275μm
[/math]

This means you would set your focus stacking software or hardware to move 1.275 µm (or smaller for finer steps) between each focus plane.

An approximation of the above formula for step size calculation that is typically used and is estimated entirely from the NA rating of the objective is given by,


[math]\large
DOF = \frac{0.00055}{NA*NA}
[/math]

This calculator assumes an 80% overlap and works well in practice. Therefore,

[math]\large
Step\,Size = DOF*0.8
[/math]