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Resolution-enhanced intensity diffraction

tomography in high numerical aperture label-free

microscopy

JIAJI LI,

1,2

ALEX MATLOCK,

YUNZHE LI,

QIAN CHEN,

LEI TIAN,

3,4

AND CHAO ZUO

1,2,

School of Electronic and Optical Engineering, Nanjing University of Science and Technology, Nanjing 210094, China

Smart Computational Imaging Laboratory (SCILab), Nanjing University of Science and Technology, Nanjing 210094, China

Department of Electrical and Computer Engineering, Boston University, Boston, Massachusetts 02215, USA

e-mail: leitian@bu.edu

*Corresponding author: zuochao@njust.edu.cn

Received 31 July 2020; revised 25 September 2020; accepted 30 September 2020; posted 2 October 2020 (Doc. ID 403873);

published 12 November 2020

We propose label-free and motion-free resolution-enhanced intensity diffraction tomography (reIDT) recovering

the 3D complex refractive index distribution of an object. By combining an annular illumi nation strategy with a

high numerical aperture (NA) condenser, we achieve near-diffraction-limited lateral resolution of 346 nm and

axial resolution of 1.2 μm over 130 μm × 130 μm × 8 μm volume. Our annular pattern matches the system’s

maximum NA to reduce the data requirement to 48 intensity frames. The reIDT system is directly built on

a standard commercial microscope with a simple LED array source and condenser lens adds-on, and promises

broad applications for natural biological imaging with minimal hardware modifications. To test the capabilities of

our technique, we present the 3D complex refractive index reconstructions on an absorptive USAF resolution

target and Henrietta Lacks (HeLa) and HT29 human cancer cells. Our work provides an important step in in-

tensity-based diffraction tomography toward high-resolution imaging applications.

https://doi.org/10.1364/PRJ.403873

1. INTRODUCTION

The refractive index (RI) of biological cells and tissues plays a

crucial role in biomedical imaging as it captures the physiologi-

cal characteristics and morphological features of a sample [1–3].

Imaging 3D biological samples with high resolution, however,

remains a challenging task. Fluorescence-based 3D imaging

methods, such as confocal microscopy [4] and multiphoton

microscopy [5], already provide excellent optical sectioning

and enable super-resolution 3D volume imaging of nanoscale

subcellular structures. Unfortunately, the exogenous labels

(e.g., dyes and fluorophores) in these techniques can be photo-

toxic and cause photobleaching due to the absorption of the

excitation light [6] and can artificially alter the sample’s behav-

ior and cellular structure [7]. Here, we introduce a resolution-

enhanced intensity diffraction tomographic (reIDT) technique

based on a conventional bright-field microscope and a high-

density LED array illumination unit with sparse annular illu-

mination. The imaging method is label-free, motion-free, fast,

and enables the high-resolution quantitative recovery of 3D in-

trinsic structural features at the single cell level.

Quantitative phase imaging (QPI) [3] is an often-used tech-

nique to recover biological cells with high contrast in their

natural states. QPI reconstructs a quantitative image of the

sample-induced two-dimensional (2D) optical path thicknesses

or phase delay based on interferometry [8–11] and noninter-

ferometry [12–18] methods. However, these phase maps evalu-

ate the sample’s total optical delay along the integrated direction

over a thin layer and provide limited volumetric information

about the object’s internal structure. To capture this informa-

tion and evaluate thicker specimens, tomographic methods

recovering 3D information are required. Recently developed

3D RI tomography techniques enable the reconstruction of

the sample’s 3D RI distribution to visualize intracellular struc-

tures, and the related 3D imaging techniques can be largely

categorized into two classes, interferometry-based and inten-

sity-only methods.

Optical diffraction tomography (ODT) is the most widely

used interferometry-based 3D QPI technique [19,20].

Standard implementations of ODT use either a rotating sample

[21] or a scanning laser beam [22–24] to capture the angle-

specific scattering arising from the sample. A 2D complex scat-

tered field containing the object’s phase and amplitude infor-

mation is directly recorded as digital interferograms under

various illumination angles, and a tomographic reconstruction

algorithm is applied to recover the sample’s 3D RI distribution.

The interferograms are captured using either an off-axis

1818

Vol. 8, No. 12 / December 2020 / Photonics Research

Research Article

[20–24]orcommonpath[25–27] holographic microscope, and

numerous ODT approaches [22–24] have been applied in bio-

medical imaging for achieving quantitative, high-resolution 3D

imaging. Hence, ODT can avoid the complex sample-prepara-

tion protocol and photobleaching effects of fluorescence while

still recovering a sample’s 3D morphology, and this label-free

3D reconstruction method has found great success in visualizing

individual unlabeled cells with quantitative refractive indices.

For intensity-only techniques, existing IDT techniques in-

volve taking multiple defocused intensity images under sym-

metric [28–31] or asymmetric [32,33] illuminations, and the

3D RI map is recovered using deconvolution [34]. Techniques

such as differential interference contrast acquire through-focus

intensity stacks to extract the 2D phase information at multiple

focus planes, and the 3D RI distribution is reconstructed using

gradient phase information [35]. Recent works further incor-

porate modulated partially coherent sources (e.g., annular shape

and Gaussian shape) to enhance the response of the 3D transfer

function for noise-robust 3D tomographic results [30,31].

However, these methods often require sample or objective

mechanical scanning along the axial direction to capture a

through-focus intensity stack. This scanning limits the setup’s

acquisition speed and requires large datasets with hundreds of

intensity frames for object recovery. Alternatively, IDT ap-

proaches have been developed allowing 3D RI information re-

covery using angle d illumination-only intensity measurements

without any mechanical scanning [36–42]. These methods ap-

ply single-scattering approximation-based models enabling

direct 3D object reconstruction with a closed-form solution

[39–41]. Iterative algorithms based on multiple scattering

models using the multislice beam propagation method have

also been developed to recover strongly scattering samples

[37,43,44]. One drawback of most of these existing techniques

is the large number of required intensity measurements that

consist of hundreds of intensity images per volume. The iter-

ative reconstruction algorithm further prolongs the whole 3D

imaging process and can become computationally expensive.

Here, we present a reIDT setup that utilizes a high-density

LED array hardware and a high numerical aperture condenser

to significantly improve the achievable resolution of the single-

scattering-based IDT technique using a larger objective

(NA

obj

 0.9). Compared to existing single-scattering-based

IDT techniques [39–41 ], we improve the imaging resolution

to near-diffraction-limited lateral resolution of 346 nm.

Specifically, the achievable axial resolution is extended from

3.4 μm to 1.2 μm enabling single-cell-level 3D structure im-

aging. By introducing a condenser lens to the setup, reIDT im-

proves the illumination efficiency and reduces the system’s

required exposure time. The annular illumination pattern op-

timally fitted with the circular microscope pupil also reduces

the image requirement to improve the system’s speed. Finally,

we show that the present technique provides high-resolution,

volumetric, subcellular information and morphology analysis

on multiple biological samples. We recover macroscale cellular

membrane structures, subcellular organelles, and micro-

organism tissues to demonstrate that our technique has poten-

tial as a fast and high-resolution 3D imaging tool for biological

samples.

2. THEORY AND METHOD

A. Principle of reIDT

As depicted in Fig. 1(a), the proposed reIDT imaging system

contains a high-density LED array illumination unit and an

Abbe condenser attached to a commercial bright-field micro-

scope. By placing the LED array in the front focal plane of

the condenser lens, each LED source located at the condenser

aperture diaphragm provides spatially partially coherent illumi-

nation in the form of a plane wave at a unique illumination

angle on the sample. The annular pattern is displayed on the

LED array, and ring-shape illumination (radius R, illumination

numerical aperture NA

illum

) is matched with the objective lens’s

pupil aperture NA

obj

properly (i.e., NA

illum

≈ NA

obj

), as illus-

trated in Fig. 1(b). The specimen is placed in the objective’s

focal plane and illuminated by each LED in the ring array.

The intensity from each illumination is recorded on a camera

which captures the interference of the object scattered field and

the unperturbed illuminating field under the single-scattering

approximation [Fig. 1(c)].

By quantifying the Fourier space information under the first

Born approximation, the phase and absorption transfer func-

tions (TFs) of the IDT linear model can be derived [39], and

the object’s complex permittivity distribution can be linearly

related to the measured intensity spectrum. The 4D TFs in

Fig. 1(d) contain slice-wise (2D) phase and absorption transfer

functions at different depths for each illumination angle, and

the exact form of the TFs can be found in Eq. (5) and Eq. (6).

Importantly, since the TFs are confined to each slice, the scat-

tering information from different sample slices is decoupled.

This decoupling allows us to use a computationally efficient,

slice-based deconvolution procedure to reconstruct the cross-

sectional RI distribution one slice at a time. The raw intensity

image set is captured by varying the illumination angles, and

each intensity spectrum of the obliquely illuminated images ex-

hibits a pair of circular Fourier regions. The pupil function fil-

ters the incoming scattered field to this circular shape, while the

oblique illumination’s transverse frequency and its conjugate

translate the scattered field in opposite directions in the fre-

quency domain [Fig. 1(e)]. The lateral cutoff frequency

envelope is indicated by the white dashed circle with the

LED source’s illumination angle (k

cutoff

 ∼2NA

obj

∕λ)in

Fig. 1(e). By combining the LED position self-calibration al-

gorithm, the accurate transverse frequency of incident illumi-

nation can be obtained and used for modeling the 4D TFs.

Finally, a fast and efficient slice-wise 3D deconvolution algo-

rithm with a closed-form solution [Eqs. (7) and (8)] is imple-

mented to recover the sample’s complex 3D RI distribution.

Since the IDT model is only valid for bright-field measure-

ments, the system still suffers from the missing cone problem

in the axial direction, resulting in the axial elongation present in

the reconstruction. Figure 1(f) illustrates the frequency support

region of the proposed reIDT method in k-space.

In practice, using a high-NA objective and illumination

scheme cannot assume paraxial imaging conditions. As pro-

posed by Sheppard and Gu et al. [45–47], high-angle micro-

scope system s usually incorporate an apodization function

introduced by the system satisfying the sine condition. Thus,

the investigation of the objective aperture function Pu

Research Article

Vol. 8, No. 12 / December 2020 / Photonics Research 1819

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