# TIRPOR - The Irrational Pursuit Of Reason

## Introduction

This page contains an interactive calculator for depth of field, effective aperture and suggested slice depth when stacking images.

The calculator is biased towards my equipment- if you have specific lenses, CoC values, apertures, etc you want adding just let me know.

You can get bogged down in theory - s the way I work is to use these values as a starting point and then check what happens in practise.

## Simple symmetric lens

First for a typical use of a reversed enlarger lens on a bellows, modelled as a symmetric lens, to give around 1 to 5x optical magnification we have:

 Parameters Equations F = lens aperture Magnification =(Si-f)/f c = circle of confusion Effective aperture = F * (1+m) m = magnification Symmetrical DOF = 2Fc((m+1)/(m^2) f = lens focal length Si = Image distance (sensor plane to lens plane)
 User parameters> Calculated values Circle of Confusion 10 um 15 um 20 um (Nikon D200) 25 um 30 um (Nikon D700) 35 um Optical Magnification Lens focal length 35mm 38mm 40mm 50mm El-Nikkor 50mm f2.8N reversed 80mm Effective aperture Sensor to lens (Si) 25mm 50mm 75mm 100mm 125mm 150mm 175mm 200mm 225mm 250mm Depth of Field Lens aperture f1.8 f2 f2.8 f4 f5.6 f8 f11 f16 f22 Recommended slice (70%) Working distance for a reversed El-Nikkor 50mm f2.8N, Newtonian model, reversed planes. Other lenses may not work.

## Microscope objectives

The next case is for using microscope objectives. The ones I have available are for finite tube length Nikon ELWD and SLWD PLAN versions. the Depth of field formula is a bit different this time and takes into account the refractive index of the medium in which the sample is immersed and the wavelength we are using. I only use air (you can increase DoF by using oil or high refractive index liquids) and usually consider 550nm (or 0.55 microns) as an appropriate wavelength.

 Parameters Equations l = wavelength F = 1/(2NA) c = circle of confusion Effective aperture = F * (1+m) m = magnification DOF = (ln/NA^2) + c(n/mNA)) NA = objective numerical aperture F = lens aperture n= refractive index
 User parameters> Calculated values Circle of Confusion 10 um D200 pixel pitch 15 um 20 um (Nikon D200) 25 um 30 um (Nikon D700) 35 um Magnification Objective magnification 4x 10x 20x 40x Effective aperture NA 0.21 0.25 0.30 0.4 0.5 Depth of Field Recommended slice (70%)