Confocal Laser Scanning Microscope

1. Theory

• Definition: A confocal laser scanning microscope focuses a laser to a diffraction-limited spot, scans it across the sample and detects the returned light through a pinhole conjugate to the focus, so only light from the focal plane is recorded (Leica 2017; Zeiss).
• Optical sectioning: Light from above and below focus is defocused at the pinhole and rejected, giving thin optical sections and 3-D images (Leica 2011).
• Resolution: Lateral resolution matches or slightly exceeds widefield; axial resolution is roughly twice the lateral at high NA (Leica 2011; Leica 2017).
• Topography: In reflection, the focus position of maximum signal at each pixel gives surface height with nanometre-scale display resolution (Olympus; LNF wiki).

2. Working Principle

• Laser and scanning: A 405 $\mathrm{nm}$ laser is scanned in x and y by galvanometer or resonant mirrors (Olympus; LNF wiki).
• Pinhole and detector: A pinhole of about 1 Airy unit in front of a photomultiplier (Leica 2017; LNF wiki).
• Z scan: The objective or stage steps in focus; each pixel’s intensity peak gives its height (Olympus; peak method my reading).
• Colour imaging: A white LED and camera add a colour image for documentation (LNF wiki).

3. Applications

• Step heights and profiles: Etch depths, film steps and bump heights (LNF wiki; Olympus).
• Roughness: Surface and line roughness over lengths up to 100 $\mathrm{mm}$ (Olympus; LNF wiki).
• Volume and area: Volumes of residues and areas of features (LNF wiki).

Confocal Optics

Name	Formula	Related Formulae	Variables/Constants
Pinhole size in Airy units	$1\mathrm{AU}=\frac{1.22\lambda M}{NA}$	$D_{pinhole}\approx 1\mathrm{AU}(\text{practical choice})$	$\begin{array}{r}AU:Airyunit,theAiry-diskdiameter\\ projectedtothepinholeplane\end{array}$ $\lambda :wavelength$ $M:magnificationtothepinhole$ $\begin{array}{r}NA:numericalaperture;Leica(2017):1AU\\ asagoodpracticalcompromise,notalaw\\ ofnature,Airydiskdependingon\\ wavelength,NAandmagnification,example\\ setting0.6AU;Zeiss:Airyunitfrom\\ wavelengthandNA,themagnification\\ factortothepinholeplane(myreading)\end{array}$ $\begin{array}{r}(computed:405\mathrm{nm},100x,NA0.95gives1\\ AU=52\mu \mathrm{m}atthepinhole)\end{array}$
Lateral resolution	$d_{xy}^{wide}=\frac{\lambda }{2NA}(\text{pinhole}\ge 1\mathrm{AU})$	$FWH{M}_{xy}^{conf}\approx \frac{0.37\lambda }{NA}(\text{pinhole}\to 0)$	$d_{xy}:lateralresolution$ $\begin{array}{r}FWH{M}_{xy}:lateralpoint-spreadwidth;Leica\\ (2017):lateralresolutionequalto\\ widefieldabove1AU(d=\lambda /2NA),about30\\ percentbetteratzeropinhole,58per\\ centofthepossiblegainat0.6AU,image\\ rescanninggivingabout1.4times\\ widefield;Zeiss,Eq.8:small-pinhole\\ FWHM0.37\lambda /NA;LNFwiki:x-yresolution\\ 120\mathrm{nm}forthe405\mathrm{nm}LEXT(seetheQ/A)\end{array}$ $\begin{array}{r}(computedat405\mathrm{nm}andNA0.95:\lambda /2NA=\\ 213\mathrm{nm},0.37\lambda /NA=158\mathrm{nm})\end{array}$
Axial resolution and section thickness	$FWH{M}_z^{refl}\approx \frac{0.45\lambda }{n-\sqrt{n^2-N{A}^2}}$	$FWH{M}_z^{fluor}\approx \frac{0.64\lambda }{n-\sqrt{n^2-N{A}^2}}(\text{1 AU, approximate})$	$\begin{array}{r}FWH{M}_z:axialwidthoftheconfocalresponse\\ toamirror(reflection)orathin\\ fluorescentlayer\end{array}$ $\begin{array}{r}n:refractiveindexoftheimmersion\\ medium;Zeiss,Eq.7:fluorescenceform\\ with0.64;thereflectioncoefficient0.45\\ (myreading);Leica(2011):section\\ thicknessscalingroughlyas1/N{A}^2,about\\ doublethelateralresolutionforNAabove\\ 1,downtoabout0.5\mu \mathrm{m}influorescenceand\\ significantlythinnerforreflection,\\ measuredwithbeadsoramirror;Leica\\ (2017):zeropinholeonly25percent\\ thinnerthan1AU\end{array}$ $\begin{array}{r}(computedat405\mathrm{nm},NA0.95,n=1:265\\ \mathrm{nm}inreflectionand377\mathrm{nm}in\\ fluorescence)\end{array}$

Height Measurement

Name	Formula	Related Formulae	Variables/Constants
Height from the axial response	$z_{surface}=\arg {\max }_{z}I\left(x,y,z\right)$	${\sigma }_z\approx \frac{FWH{M}_z}{SNR}(\text{peak-fitting precision, order of magnitude})$	$\begin{array}{r}I(x,y,z):detectedintensityagainstfocus\\ ateachpixel\end{array}$ ${\sigma }_z:heightprecision$ $\begin{array}{r}SNR:signal-to-noiseratio;methodand\\ scaling(myreading);Olympus:405\mathrm{nm}\\ laser,heightresolution0.8\mathrm{nm}and\\ displayresolution1\mathrm{nm},50xheight\\ repeatability\sigma =0.012\mu \mathrm{m},heightaccuracy\\ 0.2+L/100\mu \mathrm{m},Zstroke10\mathrm{mm};LNFwiki:z\\ resolution10\mathrm{nm},heightaccuracy0.793,\\ 1.061and0.213percentat20x,50xand\\ 100x(seetheQ/A)\end{array}$ $\begin{array}{r}(computed:a265\mathrm{nm}responsewithSNRof\\ about20givesabout13\mathrm{nm},closetothe\\ 12\mathrm{nm}repeatability)\end{array}$
Height accuracy	$\Delta h=0.2+\frac{L}{100}\mu \mathrm{m}$	$\Delta x=\pm 2\text{per cent of value},3{\sigma }_{xy}=0.02\mu \mathrm{m}(100\mathrm{x})$	$\begin{array}{r}\Delta h:heightaccuracyformeasuringlength\\ Linmicrometres\end{array}$ $\Delta x:planaraccuracy$ $\begin{array}{r}{\sigma }_{xy}:planarrepeatability;Olympus:these\\ specifications,calibrationlikecontact\\ roughnessgauges;LNFwiki:periodic\\ checkswithheightstandards\end{array}$ $\begin{array}{r}(computed:a10\mu \mathrm{m}lengthgives0.3\mu \mathrm{m}anda\\ 1\mathrm{mm}length10.2\mu \mathrm{m}accuracy)\end{array}$
Maximum measurable slope	${\theta }_{max}\approx \arcsin NA(\text{specular reflection})$	$\theta >\arcsin NA\Rightarrow \text{only scattered light returns}$	$\begin{array}{r}{\theta }_{max}:steepestsurfaceslopewhosespecular\\ reflectionstillenterstheobjective;\\ geometriclimit(computed);Olympus:\\ imagingslopesupto85degrees(seethe\\ Q/A)\end{array}$ $\begin{array}{r}(computed:\arcsin 0.95=71.8degrees,\arcsin 0.60=\\ 36.9degrees,\arcsin 0.15=8.6degrees)\end{array}$

Instrument Practice

Name	Formula	Related Formulae	Variables/Constants
Field of view and stitching	$FOV=\frac{FO{V}_{1x}}{M_{obj}{z}_{opt}}$	$N_{tiles}\le 500(\text{stitching})$	$FOV:fieldofview$ $M_{obj}:objectivemagnification$ $\begin{array}{r}{z}_{opt}:opticalzoom(1to8);Olympus:\\ 5x/0.15(2560to320\mu \mathrm{m},20.0\mathrm{mm}working\\ distance),10x/0.30(1280to160\mu \mathrm{m},11.0\\ \mathrm{mm}),20x/0.60(640to80\mu \mathrm{m},1.0\mathrm{mm}),\\ 50x/0.95(256to32\mu \mathrm{m},0.35\mathrm{mm}),100x/0.95\\ (128to16\mu \mathrm{m},0.35\mathrm{mm}),total\\ magnification108xto17280x,stitchingup\\ to500images,stage100by100\mathrm{mm}(300by\\ 300option),roughnesslengthsupto100\\ \mathrm{mm};LNFwiki:6\mathrm{in}samples,10\mathrm{cm}thick,1\\ \mathrm{kg}\end{array}$ $\begin{array}{r}(computed:2560\mu \mathrm{m}x5=12.8\mathrm{mm}fora\\ nominal1xobjective;256\mu \mathrm{m}over1024\\ pixelsis250\mathrm{nm}perpixel)\end{array}$
Pinhole trade-off	$S\uparrow ,\text{sectioning}\downarrow (D>1\mathrm{AU});\text{resolution}\uparrow ,S\downarrow (D<1\mathrm{AU})$	$\Delta FWH{M}_z\left(0\to 1\mathrm{AU}\right)\approx 25\text{per cent}$	$S:detectedsignal$ $\begin{array}{r}D:pinholediameter;Leica(2017):opening\\ thepinholeaddsextrafocallightand\\ worsenssectioningwhileraisingsignal,\\ notrecommendedmerelytoreducenoise;\\ closingitimprovesresolutionbutneeds\\ efficientdetectionandnearlynoise-free\\ sensors\end{array}$ $\begin{array}{r}(computed:the25percentaxialgainat\\ zeropinholeisfrom377toabout283\mathrm{nm}\\ inthefluorescenceexample)\end{array}$

Important Questions

Ques: How does the pinhole create optical sections?

By blocking light from outside the focal plane. The laser is focused to a spot, and the returning light is imaged onto a pinhole conjugate to that spot; light reflected or emitted from above or below focus is spread over a large disc at the pinhole and mostly blocked (Zeiss: the confocal aperture prevents detection of out-of-focus light). Leica’s Borlinghaus recommends a pinhole of about 1 Airy unit, $1.22\lambda M/NA$ at the pinhole plane, 52 $\mu \mathrm{m}$ for 405 $\mathrm{nm}$ at 100x and NA 0.95 (computed), as a practical compromise rather than a law of nature. Opening it adds extrafocal light and worsens sectioning; closing it improves resolution but costs signal. In true confocal systems, Leica reports fluorescence sections down to about 0.5 $\mu \mathrm{m}$, and reflection sections significantly thinner. Reference: R. T. Borlinghaus, ‘Pinhole Effect in Confocal Microscopes’, Leica Microsystems Science Lab, 26 April 2017 (fetch-tool summary); R. T. Borlinghaus, ‘Confocal Optical Section Thickness’, Leica Microsystems Science Lab, 20 June 2011 (formula shown only as a figure) (fetch-tool summary); Carl Zeiss Microscopy, ‘Confocal Laser Scanning Microscopy: Principles’: Airy unit from wavelength and NA, lateral FWHM 0.37 lambda/NA for a small pinhole (Eq. 8), fluorescence axial FWHM 0.64 lambda/(n - sqrt(n^2 - NA^2)) (Eq. 7), confocal aperture preventing detection of out-of-focus light, 1 Airy unit the best trade-off (fetch-tool summary, equations partly garbled).

Ques: How good are confocal lateral and axial resolution?

Laterally about as good as widefield, axially much better than widefield sectioning. Leica states that with a pinhole of 1 AU or more, lateral resolution equals the widefield value $\lambda /2NA$, 213 $\mathrm{nm}$ at 405 $\mathrm{nm}$ and NA 0.95 (computed), improving about 30 per cent only as the pinhole closes to zero, where the point-spread width approaches $0.37\lambda /NA$, 158 $\mathrm{nm}$ (Zeiss, Eq. 8; computed). Axially, the reflection response from a mirror has a width of about $0.45\lambda /(n-\sqrt{n^2-N{A}^2})$, 265 $\mathrm{nm}$ here, and fluorescence sections about 377 $\mathrm{nm}$ (computed). Leica notes that section thickness scales roughly as $1/N{A}^2$ and is about twice the lateral resolution at high NA, and that closing the pinhole fully thins it only 25 per cent. Reference: R. T. Borlinghaus, ‘Pinhole Effect in Confocal Microscopes’, Leica Microsystems Science Lab, 26 April 2017 (fetch-tool summary); R. T. Borlinghaus, ‘Confocal Optical Section Thickness’, Leica Microsystems Science Lab, 20 June 2011 (formula shown only as a figure) (fetch-tool summary); Carl Zeiss Microscopy, ‘Confocal Laser Scanning Microscopy: Principles’: Airy unit from wavelength and NA, lateral FWHM 0.37 lambda/NA for a small pinhole (Eq. 8), fluorescence axial FWHM 0.64 lambda/(n - sqrt(n^2 - NA^2)) (Eq. 7), confocal aperture preventing detection of out-of-focus light, 1 Airy unit the best trade-off (fetch-tool summary, equations partly garbled).

Ques: Is the LEXT height resolution 0.8 nm or 10 nm?

The Olympus brochure gives a height resolution of 0.8 $\mathrm{nm}$ with 1 $\mathrm{nm}$ display resolution, while the Michigan LNF wiki gives a z resolution of 10 $\mathrm{nm}$ and an x-y resolution of 120 $\mathrm{nm}$. They describe different things: 0.8 $\mathrm{nm}$ is the scale or encoder step of the z drive, while 10 $\mathrm{nm}$ is closer to the practical height repeatability, which Olympus itself specifies as 12 $\mathrm{nm}$ at 50x (my reading). The practical figure is more likely to apply to real samples. The 120 $\mathrm{nm}$ lateral figure is below the 158 $\mathrm{nm}$ small-pinhole limit at 405 $\mathrm{nm}$ and NA 0.95 (computed), so it probably refers to the smallest detectable step or pixel sampling, not true resolution (my reading). Specifications should be checked against height standards, as LNF does. Reference: Olympus, ‘LEXT OLS4000 3D Laser Measuring Microscope’ brochure, hosted by IIT Madras INUP (fetch-tool summary); University of Michigan Lurie Nanofabrication Facility wiki, ‘Olympus OLS 4000 LEXT’ (fetch-tool summary).

Ques: How does a confocal microscope measure surface height?

By finding, at each pixel, the focus position that gives the brightest return. As the objective scans in z, the reflected signal at a pixel peaks when the surface is in focus, with a width of about 265 $\mathrm{nm}$ at 405 $\mathrm{nm}$ and NA 0.95 (computed), and fitting the peak locates it far more precisely than its width (my reading). With a signal-to-noise ratio of about 20, the precision is of order 13 $\mathrm{nm}$ (computed), consistent with Olympus’s 12 $\mathrm{nm}$ repeatability at 50x. Accuracy is $0.2+L/100$ $\mu \mathrm{m}$ over a measuring length L in micrometres, 0.3 $\mu \mathrm{m}$ for 10 $\mu \mathrm{m}$ (computed), and LNF’s calibration found height errors of 0.213 to 1.061 per cent depending on objective. The Z stroke reaches 10 $\mathrm{mm}$. Reference: Olympus, ‘LEXT OLS4000 3D Laser Measuring Microscope’ brochure, hosted by IIT Madras INUP (fetch-tool summary); University of Michigan Lurie Nanofabrication Facility wiki, ‘Olympus OLS 4000 LEXT’ (fetch-tool summary).

Ques: Can the confocal microscope image slopes up to 85 degrees?

Olympus advertises imaging slopes up to 85 degrees, but the specular-reflection limit is about $\arcsin NA$: 71.8 degrees for the 0.95 objectives, 36.9 for 0.60 and 8.6 for 0.15 (computed from the geometry). Steeper surfaces reflect specular light outside the objective, so only diffusely scattered light returns. On rough or textured surfaces enough scattered light reaches the pinhole to measure up to the advertised angle, while smooth steep sidewalls, such as polished etched facets, may show missing data beyond about 72 degrees (my reading). The 85 degree figure is therefore the more likely best case for scattering surfaces, and the arcsine limit the safe expectation for smooth ones. Low-NA objectives are especially limited on slopes. Reference: Olympus, ‘LEXT OLS4000 3D Laser Measuring Microscope’ brochure, hosted by IIT Madras INUP (fetch-tool summary).

Ques: How should the pinhole be set for a measurement?

Near 1 Airy unit, and not opened just to reduce noise. Borlinghaus explains that above 1 AU, intensity rises but extrafocal light and poorer sectioning come with it, so opening the pinhole to make images less noisy is not recommended; below 1 AU, both lateral and axial resolution improve, with 0.6 AU giving about 58 per cent of the possible lateral gain, but only if detection is efficient and nearly noise-free. Closing the pinhole fully would improve the section by only 25 per cent, from about 377 to 283 $\mathrm{nm}$ in the fluorescence example (computed), while the signal falls toward zero. Image rescanning gives about 1.4 times widefield lateral resolution almost independently of pinhole size. For reflection topography, signal is usually strong, so 1 AU or slightly less works well. Reference: R. T. Borlinghaus, ‘Pinhole Effect in Confocal Microscopes’, Leica Microsystems Science Lab, 26 April 2017 (fetch-tool summary).

Ques: When is a confocal microscope the right tool?

For fast, non-contact 3-D topography of micrometre-scale features. The LEXT covers fields from 2560 $\mu \mathrm{m}$ at 5x to 16 $\mu \mathrm{m}$ at 100x with an optical zoom of 1 to 8, stitching up to 500 images, and measures steps, roughness over up to 100 $\mathrm{mm}$, angles, areas and volumes (Olympus; LNF wiki). At 50x, a 256 $\mu \mathrm{m}$ field over 1024 pixels gives 250 $\mathrm{nm}$ per pixel (computed). Compared with white-light interferometry, confocal handles steeper and rougher surfaces but has coarser height resolution on smooth samples; compared with AFM, it is faster and covers larger areas but cannot resolve nanometre lateral detail (my reading). LNF accepts samples up to 6 $\mathrm{in}$ wide, 10 $\mathrm{cm}$ thick and 1 $\mathrm{kg}$. Reference: Olympus, ‘LEXT OLS4000 3D Laser Measuring Microscope’ brochure, hosted by IIT Madras INUP (fetch-tool summary); University of Michigan Lurie Nanofabrication Facility wiki, ‘Olympus OLS 4000 LEXT’ (fetch-tool summary); Optical Microscope page of this vault.

References

1. R. T. Borlinghaus, “Pinhole Effect in Confocal Microscopes,” Leica Microsystems Science Lab, Apr. 26, 2017. Available: https://www.leica-microsystems.com/science-lab/pinhole-effect-in-confocal-microscopes/
2. R. T. Borlinghaus, “Confocal Optical Section Thickness,” Leica Microsystems Science Lab, Jun. 20, 2011. Available: https://www.leica-microsystems.com/science-lab/confocal-optical-section-thickness/
3. Carl Zeiss Microscopy, “Confocal Laser Scanning Microscopy: Principles.” Available: https://www.bio.umass.edu/microscopy/Zeiss_Confocal_Principles.pdf
4. Olympus, “LEXT OLS4000 3D Laser Measuring Microscope,” product brochure, hosted by IIT Madras INUP. Available: https://inup.iitm.ac.in/assets/docus/brochure/Olympus_LEXT%20OLS%204000_Confocal_Microscope_Broucher.pdf
5. University of Michigan Lurie Nanofabrication Facility, “Olympus OLS 4000 LEXT,” LNF wiki. Available: https://lnf-wiki.eecs.umich.edu/wiki/Olympus_OLS_4000_LEXT
6. Optical Microscope, page in this vault.

Related pages in this vault: Optical Microscope, White-Light Interferometer, Atomic Force Microscope (AFM), Patterned-Wafer Optical Inspection, Scanning Electron Microscope (SEM), Scanning Near-Field Optical Microscope (SNOM) and TERS, Raman Spectrometer, Emission Microscope, OBIRCH and Lock-In Thermography, Spectral Reflectometer, Stylus Profiler.