TEM · Basics
Magnification vs resolution: why more zoom is not more detail
Start with the oil objective below and drag the magnification from 1,000× to 10,000×. The picture gets ten times bigger, but no new pair of dots splits apart.
1 Magnification vs resolution 2 Pixels per feature 3 Depth of field Takeaways Questions References
What is the difference between magnification and resolution?
Resolution d is the smallest distance at which two points still look like two; magnification only sets how big things look on your screen.
Try it: oil objective at 1,000×: the 500 nm pair is split and the 200 nm pair is one spot. Drag to 10,000×: everything is ten times bigger, but every pair closer than 240 nm (pink label) is still one blurred spot.
How many pixels do I need per feature?
A digital image keeps one brightness value per pixel, so with too few pixels across a feature it shows lines that are not there.
Try it: widen the field of view to 20 µm. Each pixel is now 19.5 nm, about one per line spacing. The recorded stripes are about 112 nm apart and turned almost 90° from the real lines.
Why do SEM images look 3D?
Depth of field is the height range that stays sharp, and the very narrow SEM beam keeps a rough surface sharp from top to bottom.
Try it: set the working distance to 20 mm. α halves to 0.75 mrad, the SEM depth of field doubles to 97 µm, and the whole 87 µm-high surface turns sharp.
What to take away
More detail: the equations, the numbers and the limits
Resolution. Light: the Rayleigh limit d = 0.61λ/NA (Born and Wolf, chapter 8; Davidson and Abramowitz), with λ = 550 nm. NA = n sinθ: n is the refractive index between lens and sample, θ the half-angle of the light cone the objective takes in. Two points d apart show a dip of about 26% between them. SEM: d = 1 nm, a best case (Joy 2012: the SEM images objects “from millimeters to below 1 nm”). At higher beam currents the probe is wider (see SEM imaging basics). TEM: 0.25 nm without a corrector (Williams and Carter give 0.25 to 0.3 nm as typical). Corrected TEM: 0.05 nm, the information limit of the TEAM 0.5 microscope (Kisielowski et al. 2008), used here as d. The information limit is the finest spacing the lens still passes into the image.
Blur shapes. Light: the Airy pattern [2J1(v)/v]2, v = 3.83 r/d, with its first dark ring at r = d. SEM and TEM: a Gaussian spot with full width at half maximum d. A TEM image forms by interference (phase contrast), so a blur spot only stands in for it.
Magnification and the eye. M = image width on the screen / field width on the sample. Every screen is viewed from 25 cm. A 20/20 eye separates points 1 arcminute apart (Tripathy and Gupta): 0.073 mm at 25 cm. The close-up adds this blur to the instrument blur. For a light microscope the useful range is 500 to 1000 × NA (Davidson and Abramowitz, who say the 500 is set “rather arbitrarily”). With d = 0.61λ/NA and λ = 550 nm, that range puts d at 0.17 to 0.34 mm on the screen for any NA. The page uses the same 0.17 to 0.34 mm for the SEM and TEM; that step is its own.
Pixels. Shannon's sampling theorem: a pattern is fully recorded if it is sampled at least twice per period of its finest detail. In microscopy the usual pixel is half the resolution (Pawley 2000). Pawley’s handbook chapter suggests 2.3 to 2.8 pixels per resolved distance, because features also run diagonally. With fewer than 2 per period the samples show a false, coarser pattern (aliasing). The page samples each pixel at its centre, as an SEM does when its probe is smaller than a pixel. Line contrast after a Gaussian blur: exp(−π2d2/(4 ln2 · s2)). The over-sampled cut-off, 4 pixels per resolution distance, is the page’s own choice.
Depth of field. A cone of half-angle α spreads a point Δz out of focus into a disc 2αΔz wide. If the eye misses blur smaller than δ = 0.073 mm/M on the sample, the sharp depth is D = δ/α. SEM: α = aperture radius / working distance, for a final aperture at the objective lens. Joy (2012) gives the same 1/α trend, and Goldstein et al. treat SEM depth of field in section 4.2.6. Light: D = λn/NA2 + nδ/NA (Levoy et al., eq. 4, after Inoué and Oldenbourg), dry objectives, n = 1. Its second term is the small-angle cone rule, so at NA 0.95, where the cone is wide, the light values are estimates.
Limits. The beam cannot be much narrower than about λ/α (Joy 2012): 6.6 nm at 15 kV (λ = 9.94 pm) with α = 1.5 mrad. The page warns when that is larger than δ. Aberrations, the spread of electrons in the sample, noise and drift are left out. The test surface is a sum of waves plus one step, scaled so its height range is a set share of the field width.
Questions people ask
What is the difference between magnification and resolution?
Magnification is how much bigger the image is than the object. Resolution is the smallest distance at which two points still show as two. A 1.4 NA oil objective resolves about 240 nm in green light at any magnification; magnifying more only makes that 240 nm look bigger.
What is empty magnification?
Magnification past the point where the finest resolved detail is already easy to see. The image grows, but no new detail appears. For a light microscope the textbook limit is 1000 × NA (Davidson and Abramowitz), so 1,400× for a 1.4 NA objective.
What is the resolution limit of a light microscope?
About d = 0.61λ/NA, the Rayleigh limit; NA (numerical aperture) says how wide a cone of light the objective collects. In green light (550 nm) that is 1.34 µm at NA 0.25, 353 nm at NA 0.95 and 240 nm with a 1.4 NA oil objective. A shorter wavelength or a higher NA gives a smaller d.
Why can electron microscopes resolve smaller things?
Electrons have a far shorter wavelength: 2.5 pm at 200 kV, over 200,000 times shorter than green light. Electron lenses have large aberrations, so a TEM typically resolves 0.25 to 0.3 nm without a corrector. The best corrected TEM passes detail down to 0.05 nm.
Why use a scale bar instead of a magnification number?
Magnification depends on how big the image is shown. An image of a field 290 µm wide is 224× on a phone and 2,070× on a 27-inch monitor. A scale bar is part of the image, so it stays right on any screen or print.
How many pixels do I need per feature?
At least 2 pixels per period of the finest detail you want to record (Nyquist). A common target is 2 to 3 pixels per resolution distance. With 1024 pixels and a 3 nm probe, that means a field of view below about 1.5 µm.
Why do SEM images look 3D?
Two reasons. The beam is a narrow cone, so its depth of field is large. At 1,000× with a 30 µm aperture at 10 mm, 48 µm of height is sharp. And the secondary-electron signal is stronger from slopes and edges, so the surface looks lit from the side (see SEM imaging basics).
Does a higher magnification give a better image?
Only until the finest detail is easy to see. Past that you get a smaller field with the same detail. In an electron microscope, ten times the magnification at the same current and scan time also puts 100 times more electrons on each square micrometre.
Related: SEM imaging basics (probe size and noise) · Aberration correction · HRTEM and FFT guide · TEM scattering guide · EBSD step size and KAM (step size is the pixel size) · Electron beam contamination (the dark square where you scanned) · What the electron saw
References
Show the 12 references
- M. Born and E. Wolf, Principles of Optics, 7th ed., Cambridge University Press (1999): chapter 8 (resolving power of a microscope). doi:10.1017/CBO9781139644181
- C. E. Shannon, Communication in the presence of noise, Proceedings of the IRE 37, 10 to 21 (1949). doi:10.1109/JRPROC.1949.232969
- M. W. Davidson and M. Abramowitz, Optical microscopy, in Encyclopedia of Imaging Science and Technology, Wiley (2002). doi:10.1002/0471443395.img074
- J. Pawley, The 39 steps: a cautionary tale of quantitative 3-D fluorescence microscopy, BioTechniques 28, 884 to 887 (2000). doi:10.2144/00285bt01
- J. B. Pawley, Points, pixels, and gray levels: digitizing image data, in Handbook of Biological Confocal Microscopy, 3rd ed., Springer (2006), pp. 59 to 79. doi:10.1007/978-0-387-45524-2_4
- M. Levoy, R. Ng, A. Adams, M. Footer and M. Horowitz, Light field microscopy, ACM Transactions on Graphics 25, 924 to 934 (2006): eq. 4 (depth of field), after S. Inoué and R. Oldenbourg, Handbook of Optics, 2nd ed. (1995). doi:10.1145/1141911.1141976
- J. I. Goldstein, D. E. Newbury, P. Echlin, D. C. Joy, C. E. Lyman, E. Lifshin, L. Sawyer and J. R. Michael, Scanning Electron Microscopy and X-ray Microanalysis, 3rd ed., Springer (2003): chapter 4, sections 4.2.3 to 4.2.6 (magnification, pixel size, depth of field). doi:10.1007/978-1-4615-0215-9
- D. C. Joy, SEM for the 21st century: scanning ion microscopy, Metallography, Microstructure, and Analysis 1, 115 to 121 (2012). doi:10.1007/s13632-012-0013-0
- D. B. Williams and C. B. Carter, Transmission Electron Microscopy, 2nd ed., Springer (2009): chapter 6, p. 108. doi:10.1007/978-0-387-76501-3
- C. Kisielowski et al., Detection of single atoms and buried defects in three dimensions by aberration-corrected electron microscope with 0.5-Å information limit, Microscopy and Microanalysis 14, 469 to 477 (2008). doi:10.1017/S1431927608080902
- K. Tripathy and A. Gupta, Evaluation of visual acuity, StatPearls, StatPearls Publishing (updated 2024), NCBI Bookshelf NBK564307.
- E. Tiesinga, P. J. Mohr, D. B. Newell and B. N. Taylor, CODATA recommended values of the fundamental physical constants: 2018, Reviews of Modern Physics 93, 025010 (2021): constants for the electron wavelength. doi:10.1103/RevModPhys.93.025010
BibTeX
@misc{tripathy2026magnificationresolution,
author = {Tripathy, Manisha},
title = {Magnification vs Resolution Lab},
year = {2026},
howpublished = {\url{https://untetheredatom.com/tem/magnification-vs-resolution}},
note = {Interactive web tool}
}