Microscope depth of field (source code)

= Microscope depth of field

The <microscope depth of field> is the range of specimen depths judged acceptably sharp for a fixed imaging configuration and focus setting. It is an object-space tolerance defined by a sharpness criterion. It differs from <microscope working distance>, a physical clearance, and from image-space <depth of focus>. The accepted range depends on <numerical aperture>, wavelength, detector/display sampling and the criterion used to judge blur.

An original geometric model makes the criterion explicit. Let a local light cone have object-side half-angle $\alpha$. An axial defocus $\Delta z$ gives blur diameter approximately $b_{\rm blur}=2|\Delta z|\tan\alpha$. If acceptable object-space blur diameter is at most $b$, the symmetric depth range is
$$
|\Delta z|\le\frac{b}{2\tan\alpha},\qquad
D=\frac{b}{\tan\alpha}.
$$
This cone model ignores diffraction and aberrations; it provides a stated geometric estimate, not a universal microscope specification.

For $b=2\,\mathrm{\mu m}$, refractive index $n=1$ and <numerical aperture> $n\sin\alpha=0.25$, the total range is about7.75µm. Raising the aperture to0.50 with the same blur criterion reduces it to about3.46µm. The manufacturer's iris discussion describes this tradeoff qualitatively: closing the aperture increases depth of field while reducing resolving power.<Labeling of Objectives by Leica Microsystems>[“Numerical Aperture”; “Iris Diaphragm”, depth-of-field/resolution tradeoff]{ref}

In a diffraction-limited comparison, choosing a tolerable blur scale proportional to $\lambda/\mathrm{NA}$ and using $\tan\alpha\approx\mathrm{NA}/n$ at small angle yields a depth scale proportional to $n\lambda/\mathrm{NA}^2$. The prefactor depends on the stated sharpness criterion. It should not be treated as one exact range independent of contrast, sampling or the way the image is assessed.

For a simple acceptance example, suppose the adopted total range is6µm and a nominally flat inspected surface varies from−4 to+4µm about a center focus. The8µm extent does not fit inside that6µm interval. Moving focus shifts which parts qualify but does not increase the interval width. A larger-looking image also does not prove better <diffraction-limited resolution> or a larger axial acceptance range.

Record whether a quoted depth is total or one-sided, and keep the optical configuration and blur/contrast criterion with it. Otherwise two reported values can differ because they describe different acceptance tests rather than different objective performance.