Technology Note

Transport of Intensity Equation (TIE)A New Brightfield Method for Imaging and Fast Autofocusing
During Automated Slide Scanning with ZEISS Axioscan 7

Authors: Dr. Markus Neumann, Dr. Markus Sticker, Dr. Volker Döring		

Carl Zeiss Microscopy GmbH, Jena, Germany		

Dr. Christoph Husemann		Corporate Research and Technology, ZEISS GroupDate:

September 2023

The use of focus maps as an autofocus technique for high-throughput, whole slide imaging
experiments is widely adopted but has many disadvantages when applied to fluorescently labeledsamples. ZEISS has implemented a new brightfield contrast technique, Transport of Intensity Equation(TIE), with the ZEISS Axioscan 7 digital slide scanner. TIE overcomes previous challenges providing fastand reproducible autofocusing without compromising fluorescence imaging quality as well as offering
additional contextual data.

Introduction
Efficient scanning for whole slide imaging of tissue sections

With fluorescently labeled tissues, a fluorescent counterstain,

requires high-throughput, automated protocols. These methods

such as DAPI, which labels all cell nuclei that are typically distrib-yield higher levels of data collection for more thorough analyses

uted throughout the tissue section, can be used to generate aand lower hands-on requirements which improves time manage-

focus map. However, repeated DAPI imaging can cause bleach-ment of laboratory researchers and staff. However, the successing, particularly with sensitive fluorescent labels typically usedof these experiments relies on the imaging system’s ability towith multiplex experiments. Additionally, using fluorescenceaccurately and consistently autofocus as it collects hundreds toillumination to find the focal point often takes longer comparedthousands of images.

to using brightfield illumination and, when working with hundreds to thousands of images, the length of the experiment can

One commonly used method for autofocusing is the use of abecome unmanageable. One might consider using brightfield

focus map, which is created by pre-scanning the selected area,

illumination with contrast enhancing methods, such as phasesampling axial focus points, and using an algorithm to automat-contrast or DIC. However, these methods require additional

ically determine the axial position with the sharpest image. This

optical elements in the light path: matching phase rings in themethod works well with brightfield illumination and chromo-condenser and objective for phase contrast or Wollaston prisms

genically stained slides; however, this method has disadvantages

and analyzers for DIC. Not only do these components add towhen moving to fluorescently labeled samples.

the overall cost and complexity of the imaging system, but theirpresence in the light path negatively impacts the quality offluorescence imaging.
To address these challenges, ZEISS has implemented theTransport of Intensity Equation (TIE) contrast enhancing methodwith the digital slide scanner ZEISS Axioscan 7. This brightfieldtechnique avoids bleaching by using the transmitted light sourceand does not reduce the fluorescence imaging performance as
no additional optical elements are introduced into the fluorescence light path. Now the advantages of fast sample detection
and focus mapping can be combined with the highest quality
fluorescence imaging for challenging whole slide imaging experiments, including those using multiplexing or other sensitive

Figure 1 ZEISS Axioscan 7

fluorescent labels.

2Overview of the Transport of Intensity Equation (TIE)

TIE can be used to determine the sample focus quickly andTIE creates digital contrast images by acquiring three images

reliably for thin, transparent samples, as shown in Figure 3.

in transmitted light brightfield while closing the aperture ofA focus stack is acquired quickly using the ZEISS Axioscan 7

the condenser completely to create an almost coherent bundle

flash illumination method followed by a software calculationof light. The three images are each separated by one depth offor image sharpness for each focus plane.

field (DOF) in the axial direction: one image is from the planeof focus, one from above, and one from below, as shown in

5× / 0.15 Step 69.16

Figure 2. The raw images are then processed, resulting in either

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a phase contrast image or a relief contrast image, reminiscent of

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differential interference contrast (DIC).

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Out of focus
1 DOF

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0Focus Position

TIE-Phase

Figure 3 Results for one focus support point determined in the coarse focus(top) and the fine focus map (bottom) creation results when using TIE contrast.
X-axis: focus position. Y-axis: result of focus merit (image sharpness) calculation.

TIE for Fast and Efficient Autofocusing
A major advantage of the implementation of TIE with ZEISSAxioscan is the ability to use it for fast and efficient autofocusingwith the rapid acquisition method using flashed illumination.1
Very brief pulses of illumination from a very bright white light
LED are synchronized with the camera acquisition while moving
the focus axis in a continuous fashion. In typical scenarios,
acquiring a full stack followed by the calculation will not take

TIE-Relief

more than a few seconds per focal point.
This speed increase is significantly higher over traditional focus
determination using the fluorescent DAPI channel, which is typically ~20 seconds. Additionally, TIE also avoids photodamage tofluorescent dyes in the sample as well as the undesired artifactsof darker tiles for the DAPI channel during samples acquisition.

Figure 2 Working principle of TIE contrast. Phase contrast or relief contrast are

Such artifacts can also cause problems for automated image

two visual representations of TIE.

analysis.

3While TIE is ideally used for very thin

Conclusion

difference via interference. There aretranslucent samples with low contrast,

To meet the need for efficient autofocus-numerous techniques reviewed in thesuch as monolayer cell cultures (< 3 µm)

ing for automated, whole slide imaging

literature to image the phase propertiesor thin tissue sections (< 5 µm), it has alsoof fluorescently labeled samples thatof a sample, ranging from classical phasebeen shown to be useful when scanning

does not cause photobleaching or reduce

contrast 2 and holographic methods 3 tothicker (> 5 µm) tissue sections.

image quality, ZEISS has implemented TIE

illumination diversification 4 and wave-

as a novel brightfield contrast method

front sensors5. TIE is built on the fact that

TIE Provides Additional Contextual

with the ZEISS Axioscan 7 digital slide

phase information becomes visible after

Information during Data Collection

scanner. Not only does TIE meet thesesome propagation in free space because

As a main transmitted light contrast

needs, it can also be used to provide

of interference of best focus light withmethod with ZEISS Axioscan 7, TIE adds

additional structural context to fluores-

the change of the light field in the defo-

the ability to create phase contrast

cence data.

cused images. In a paraxial approximationfor coherent illumination, this change isand relief contrast images during datacollection. This provides contextual infor-TIE is a valuable addition to ZEISS Axio­

reduced to a gradient and leads to themation, particularly with fluorescencescan 7, a high-performance slide scanner

following transport of intensity equation

experiments. This is demonstrated inwith unsurpassed fluorescence imaging(TIE)

Figure 4. Mouse kidney tissue was stained

quality for high-throughput, complex

with DAPI and Alexa 647 (Phalloidin). TIE

experiments.

provides a nice phase contrast, which=1()

can be combined with the fluorescence

Supplementary Information:

first discovered by Teague 6, which relates

information to show where the nuclei

Theoretical Backgroundthe gradient of the phase φ to theand actin structures are positioned inThe phase information of the propagatedchange of intensity along the optical axis

relationship to the glomeruli.

light wave becomes visible as intensity. Here k is the wavelength dependent
wave number and I is the best focus
intensity.
By recording focal stacks, ZEISS Axioscan 7
measures the intensity in several planes.
The best contrast is obtained by reducing
the aperture of the condenser to a verysmall value, e.g., to 0.07 NA. We approximate

by the change of the brightnessof the images between adjacent planes in
the focal stack. Optimal lateral resolution
is obtained if the distance between adjacent planes corresponds to one Rayleighunit ~ / NA. If the sample has only small

phase differences, it can be useful to uselarger distances. Following Paganin andNugent7, we directly solve the TIE withthe help of Fourier transformation. To
avoid periodic artefacts, boundary pixels
are padded internally. Since slowly varying parts of the phase become visible inintensity only after a longer propagation
distance, we apply a small high pass filter
to reduce low frequency artefacts.
Figure 4 Mouse kidney tissue section stained with DAPI and Alexa 647 (Phalloidin). A) DAPI fluorescence,Having obtained the phase image, weB) Phalloidin Alexa 647 fluorescence, C) TIE-Phase contrast, D) Merge fluorescence and TIE Phase. Image

can also calculate a gradient phasecourtesy of Katarzyna Dobaczewska, Microscopy and Histology Core Facility, La Jolla Institute for
Immunology, San Diego, USA.

image, which resembles the contrast ofa DIC image. Therefore, we call it reliefcontrast.
4

For a comparison, see Figure 5 wherebrightfield (A), DIC (B), and relief (C) areA

BCD

shown together. The gradient of thephase can be calculated for any direction
as it is possible to adjust the direction of
the gradient in post-processing after theimage has been acquired, which corresponds to a rotation of the Wollaston
prism in traditional DIC.
The TIE was originally derived for acoherent setting in a paraxial approximation. Only with this boundary condition
can the result be rigorously interpreted
as a phase of an electromagnetic wave
with quantitative meaning. However, theequation can describe paraxial intensity
transport for partially coherent light inthe context of Wigner distribution functions 8. And even for incoherent light theTIE describes the conservation of energy
for moments of non-paraxial light fields 9.
Therefore, we apply the TIE also for highnumerical aperture and partially coherent
illumination, which gives good contrast,

Figure 5 FluoCellsTM No.1 (BPAE). A: Brightfield; B: DIC; C: TIE-relief; D: fluorescence.

but a direct quantitative interpretation of
the phase would require further calibration, which is not currently available for
ZEISS Axioscan 7.
A practical example is shown in Figure 6.
Potato starch granules are shown in asection of potato tissue. While showing
relatively low contrast in brightfield, thecontrast is markedly enhanced both in thephase and the relief contrast version ofFigure 6 Transmitted light images of potato starch. Left: TIE-Phase. Middle: TIE-Relief. Right: Brightfield.

the TIE results.

References:[1] https://worldwide.espacenet.com/patent/search?q=pn%3DUS2022252856A1[2] D ifferential Interference Contrast (DIC), Zernike Phase Contrast…
[3] G . Popescu, “Quantitative Phase Imaging of Cells and Tissues” McGraw Hill Professional (2011)[4] Z heng, G., Horstmeyer, R. & Yang, C. Correction: Corrigendum: Wide-field, high-resolution Fourier ptychographic microscopy. Nature Photon 9,621 (2015). https://doi.org/10.1038/nphoton.2015.148[5] P ierre Bon, Guillaume Maucort, Benoit Wattellier, and Serge Monneret, “Quadriwave lateral shearing interferometry for quantitative phasemicroscopy of living cells,” Opt. Express 17, 13080-13094 (2009)[6] M . R. Teague, Opt. Soc. Am. 73, 1434-1441 (1983), https://doi.org/10.1364/JOSA.73.001434[7] D. Paganin and K. A. Nugent, Phys. Rev. Lett. 80, 2586 (1998), https://doi.org/10.1103/PhysRevLett.80.2586[8] C. Zuo et al (2015). Transport of intensity phase retrieval and computational imaging for partially coherent fields: The phase space perspective.
Optics and Lasers in Engineering. 71. 10.1016/j.optlaseng.2015.03.006.
[9] A . Orth and K. B. Crozier, “Light field moment imaging,” Opt. Lett. 38, 2666-2668 (2013)

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