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 $b_{\mathrm{blur}}=2|\Delta z|\tan \alpha$. If acceptable object-space blur diameter is at most $b$, the symmetric depth range isThis cone model ignores diffraction and aberrations; it provides a stated geometric estimate, not a universal microscope specification.

For $b=2\mu \mathrm{m}$, 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.^[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.