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\chapter{A Simple and Inexpensive Holographic Microscope for Biological Imaging}
\label{chap:simple-dhm}

\newthought{Recent advances in optical microscopy} have led to enhanced
resolution and sensitivity, but at the cost of simplicity and portability.
Although modern microscopes can optically section a sample, detect single
molecules, and even break the diffraction limit, they are still bulky
instruments costing tens or hundreds of thousands of dollars. This often puts
the modern optical microscope in a time-shared central facility instead of in
every lab. Common add-ons such as environmental chambers, micromanipulators, or
microfluidic devices further drive up costs and complicate sharing. But for many
experiments in biology, materials science, and physics that do not require all
the features offered by the latest generation of microscopes, it makes more
sense to use simpler, cheaper microscopes that can be added onto other
specialized apparatus. Such ``commodity'' could enable new experiments
and even new applications for microscopy. They could also help make advanced
imaging available to laboratories in the developing world, to small businesses,
and to students.

Coherent imaging methods such as holography may be the most promising route to
simple microscopes. Holographic microscopy is a widefield phase imaging
technique similar to differential interference contrast and phase contrast
microscopy. It captures information about both the phase and amplitude of light
scattered from a sample. As a result, a relatively simple optical setup, in
conjunction with a modern desktop computer, can create and visualize
three-dimensional reconstructions of a sample \cite{schnars_digital_2002}.
Unlike conventional widefield microscopes, the image given by holographic
reconstruction is linearly related to optical path lengths. This allows
holography to avoid the contrast artifacts introduced by traditional widefield
phase techniques, thereby enabling quantitative interpretation of the images.
Furthermore, the enhanced depth of field of holographic microscopes eliminates
the need to change focus. Thus, a low cost holographic microscope can compete
favorably with standard widefield microscopy for many applications.

Holographic microscopes are especially advantageous for three-dimensional (3D)
imaging. Compared to the current standard for 3D microscopy, the confocal
microscope, a holographic microscope is much simpler, requiring no moving parts
to obtain a 3D image, and potentially much faster, because a 3D reconstruction
can be obtained from a single 2D image. Holography therefore offers a low cost,
less invasive alternative to confocal microscopy for three-dimensional imaging
of samples where chemically specific labeling is not needed.

Here we show how advances in semiconductor technology have made it
possible to build an inexpensive, self-contained, compact digital
holographic microscope with good resolution and large depth of
field. Our microscope uses conventional optical parts, an inexpensive
diode laser, a hobbyist microcontroller board, and a consumer grade
digital camera. The parts can be purchased on eBay or hobbyist
websites for a total cost of less than \$1000. Reconstruction is done
on a standard desktop computer. The microcontroller synchronizes the
laser and camera so that the sample is exposed to light for only
80~\si{\nano\second} per hologram, resulting in a total exposure of
about 20~nJ of laser light, compared to tens of millijoules for a
typical 3D confocal stack \cite{pawley_handbook_2006}. At the same
time, the microscope requires no pinholes or spatial filters, making
it easy to align and robust to vibration. We show that the instrument
can take 3D images of living cells and colloidal particle suspensions
with a resolution better than 3~\si{\micro\meter} and a depth of field
of more than 150~\si{\micro\meter}.

Early holographic microscopes required precision equipment such as water-cooled lasers, spatial filters, and vibration isolators, but diode lasers and CMOS detectors have made these components unnecessary. In many ways a diode laser is an ideal light source for microscopy; it gives a high-quality, narrow-band, easily collimated beam from a compact, efficient illumination source. Lasers have not seen much use in widefield microscopy because their long coherence length imposes coherent noise and interference fringes. But in holography coherence becomes an advantage, allowing the extraction of phase information. Laser diodes suitable for holographic microscopy are now mass-produced for consumer electronics such as CD writers and laser printers. At the same time, CMOS detectors with pixel density sufficient to capture fine interference patterns with only modest magnification are now available in mass-market cameras, and modern desktop computers can reconstruct the captured megapixel holograms in less than a second. The combination of a pulsed laser diode and sensitive camera allows fast exposures that eliminate the need for vibration isolation.  This confluence of technologies enables us to construct a “commodity” microscope with nonetheless impressive capabilities.

Holographic microscopes have been used to study biological systems, but the instruments are more complicated and more expensive than the one we show here. These other approaches include both off-axis and inline configurations. Off-axis microscopes can more easily achieve high resolution, but because they have two optical paths, they are sensitive to vibration and require careful alignment~\cite{depeursinge_digital_2007, dubois_improved_1999, emery_dhm_2007, mann_movies_2006}. Inline holography generally involves a simpler optical train. Lensless versions of inline holographic microscopes have been developed for a few applications in biology, particularly analysis of swimming microorganisms~\cite{jericho_submersible_2006, kreuzer_digital_2001, lewis_swimming_2006, repetto_lensless_2004, xu_digital_2001, xu_tracking_2003}. These lensless instruments can be quite simple, but they impose restrictions on the geometry of the apparatus, and they require imaging cameras with very high resolution. Therefore many recent inline apparatuses for examining eukaryotic cells or small particles use an objective lens~\cite{choi_three-dimensional_2009, moon_automated_2009, satake_measurements_2006, sheng_digital_2006, sheng_digital_2007}. We choose to use an inline configuration with an objective lens because it allows us maintain good resolution while using a consumer-grade digital camera for imaging.

Other holographic microscopes have been constructed to be simple and low-cost,
but ours is distinct in that it achieves these goals without a significant
tradeoff in image quality or resolution. Thus, although simple microscopes can
be made with lensless design and LED illumination~\cite{repetto_lensless_2004},
we choose to use a laser diode, which, while more expensive than an LED, has a
high coherence length at a cost ($\sim$\$40) that is still small compared to that of a
digital camera. An instrument recently developed by Seo and coworkers~\cite{seo_lensfree_2009} also focused on simplicity, low cost, and
biological imaging, but as the authors note, the instrument is engineered for
cytometry, not high-resolution imaging.

Our instrument has two other distinguishing features. First, acquisition is self-contained: the instrument is internally powered and internally controlled, and it stores images on-board. This allows it to operate autonomously in a closed or remote space. Second, we use consumer and hobbyist components throughout to keep the cost low and position the microscope to benefit from the rapid improvements in these technologies. The result is a simple, flexible and inexpensive instrument that can be incorporated into another experiment or apparatus at minimal cost and effort.

\section{Methods}

\subsection{Design of the holographic microscope}

Our instrument uses an in-line configuration~\cite{goodman_introduction_2005} comprising only a laser, camera, objective, sample stage, beam telescope and microcontroller, as shown in Figure~\ref{fig:sdhm-diagram}. Twin-image effects are minimized because our samples are relatively thin (tens or hundreds of \si{\micro\meter}) compared to the optical distances (multiple mm).
\begin{figure}
  \centering
  \includegraphics[width=4.75in]{figures/simple-dhm/diagram}
  \caption{a) Microscope diagram, showing optically relevant distances such as that between the objective and the camera sensor.  The beam is approximately collimated entering and exiting the beam telescope.  b) Photograph of microscope.  c) Drive circuitry for the ADL 78901 laser diode.  The 1 M$\Omega$ resistor and 1 nF capacitor protect the laser diode from current spikes.  The 5.5~\si{\kilo\ohm} resistor and 1 nF capacitor smooth the Arduino Pulse Width Modulation (PWM) output into an analog voltage.  The 2N3904 Transistor controls current through the diode.}
  \label{fig:sdhm-diagram}
\end{figure}

A battery powered 785~\si{\nano\meter} ADL 78901 laser diode provides illumination. This diode outputs a single transverse mode and has a measured coherence length in excess of 5~\si{\centi\meter}. For the images shown here, we used either 2.3 mW of laser power and 80~\si{\micro\second} pulses or 0.235 mW and 20~\si{\milli\second} pulses. We measured the power with a Thorlabs PM 100 power meter. An aspheric lens collimates the diode output, and a 3.75$\times$ beam-expanding telescope provides uniform illumination across the objective aperture. We did not need to incorporate a spatial filter because the diode produces a beam of sufficient quality. This greatly simplifies alignment.

A battery-powered Arduino board (Adafruit Industries) employing an Amtel ATMega 168 microcontroller controls both the laser and the camera. An analog output on the microcontroller drives a switching transistor which controls power to the laser (Figure 1c). Because the diode is on for only a short time per exposure, no temperature control is needed. The microcontroller also triggers the camera shutter using the camera's external shutter release port. Using a microcontroller for these functions allows us to program arbitrary sequences with varying illumination and frame timing. The programs can be uploaded to the microcontroller from a desktop computer using a USB port.

Samples are mounted to a 3-axis micrometer stage for translation and focusing, and a 20$\times$, 0.4 NA Newport objective magnifies the hologram. We take care to keep all optics free from dust and fingerprints since light scattered off these blemishes adds additional noise fringes.  Because we use only collimated or weakly diverging beams, there are wide tolerances on most of the optical distances.

We record holograms with a Canon EOS 6.3 megapixel 300D digital SLR camera. This camera has a 3088$\times$2056 pixel (22.7~\si{\milli\meter}$\times$15.1~\si{\milli\meter}) CMOS sensor with 7.35~\si{\micro\meter} square pixels. Like most consumer cameras, it has an IR blocking filter. We removed this filter using the procedure given in [21] to obtain good sensitivity with our 785~\si{\nano\meter} light source.  To minimize interference fringes from lens reflections, we image light from the objective directly onto the CMOS sensor. We store the images as RAW files on an 8 GB Compact Flash II 133X card (Kingston Technology). Although the camera can take a burst of up to four images in a little over a second, it requires about 15 seconds to save each image to the memory card. Newer consumer cameras store images significantly faster than our five-year old model.

The camera, microcontroller, and laser are all battery powered so that the instrument can acquire data without any outside connection. Ate the end of an experiment, we transfer the holograms to a desktop computer for reconstruction.

\subsection{Reconstruction}
We use the convolution method to reconstruct holograms~\cite{schnars_digital_2002}. The reconstructed image is

\begin{equation}
  \Gamma(\xi, \eta, d) = \int^\infty_{-\infty} h(x, y) g(\xi, \eta, x, y, d) dx\, dy
\end{equation}
where $h$ is the observed hologram and $g$ is the impulse response at a distance $d$.  This equation contains two sets of planar coordinates: $x$ and $y$ describe the position at the sensor, and $\xi$ and $\eta$ describe the position in the reconstructed image. The impulse response $g$ is
\begin{equation}
  g(\xi, \eta, x, y, d) = \frac{\frac{i}{\lambda}\exp\left(i\frac{2\pi}{\lambda}\sqrt{d^2 + (x+\xi)^2 + (y+\eta)^2}\right)}{\sqrt{d^2+(x+\xi)^2+(y+\eta)^2}}
\end{equation}
where $\lambda$ is the wavelength in medium. The reconstruction, $\Gamma$, is a complex two dimensional array whose elements represent both phase and amplitude of the reconstructed field. The amplitude can be extracted as $|\Gamma|$, and the phase as

\begin{equation}
  \phi(\xi, \eta, d) = \arg(\Gamma).
\end{equation}

Phase extraction is useful because many objects, including biological cells, are weakly absorbing but have spatially varying indices of refraction. Although these samples have little effect on the amplitude of transmitted light, they introduce a noticeable phase shift. Phase images therefore frequently give better contrast for biological materials. When reconstructing a phase image we examine reconstructions closely spaced over half a wavelength to determine which phase gives the best contrast for the features of interest. We then reconstruct a volume by stepping integer multiples of the wavelength from that distance, maintaining the same relative phase and therefore the same contrast.

As discussed in a paper by Sheng and coworkers~\cite{sheng_digital_2006}, to a good approximation the effect of the lens is simply to rescale the lateral dimensions of the hologram by the objective magnification. We account for this effect by reducing the dimensions of the numerical pixels used in reconstruction by the same factor.  Thus we reconstruct as if we had a detector with 0.34~\si{\micro\meter} pixels that lies at the focus of the objective. The reconstruction distance $d$ is then measured from where the effective detector lies.

We extract RAW images from the camera to 24-bit, 3-channel TIFF files using the \verb+dcraw+ software package~\cite{coffin_decoding_2010}. We use only the red channel in analysis because it has the highest sensitivity to IR illumination. In order to obtain a square image suitable for fast Fourier transforms, we extract a 1024$\times$1024 or 2048$\times$2048 pixel subimage centered on features of interest. We perform reconstructions on a desktop computer with a 3~GHz Intel Core 2 Duo CPU using custom software written in Python with the SciPy numerical library~\cite{oliphant_scipy_2001}.

\subsection{Sample preparation}

We used a USAF 1951 resolution test target (Edmund Optics) to measure the resolution of the microscope. The target consists of line groups of decreasing size; the size of each group is given by a table from the manufacturer’s website. We determine resolution by examining the reconstructed image and finding the smallest element where the lines are distinct.

We show images from two types of samples: microsphere suspensions and living cells. The microsphere samples consist of 2~\si{\micro\meter} Invitrogen sulfate latex particles in Knox Gelatine.  We prepared gelatin with one gram of Gelatine powder per 40 mL of tap water, and added $\sim$100~\si{\micro\liter} of 8\% w/v particles to $\sim$100 mL of gelatin solution. We made a thick sample (several hundred micrometers) using silicon vacuum grease (Dow Corning) as a spacer between a standard microscope slide and a number one cover slip. We flowed hot gelatin-particle solution into the gap by capillary action and then sealed the cover slip to the slide using five minute epoxy. The gelatin then cools and solidifies, preventing the particles from sedimenting or diffusing.

The living cell samples are wet mounts of cheek cells (Squamous Epithelium) obtained from swabbing the inside of the mouth. The cells from the swab were placed on a microscope slide, diluted in tap water, and covered with a number one cover slip. Because we did not use an isotonic buffer, we imaged the cells within thirty minutes of mounting, before they were lysed by the hypotonic medium.

\section{Results and Discussion}
Using the USAF resolution grid shown in Figure~\ref{fig:usaf-resolution}, we measured the resolution of our reconstructed images to be about 2.8~\si{\micro\meter}.  Resolution in a holographic microscope is limited both by the diffraction limit of the microscope objective used and by the ability of the camera to detect and resolve closely spaced interference fringes. The theoretical resolution for our 0.4 NA objective is about 1~\si{\micro\meter} resolution with 785~\si{\nano\meter} light. Therefore the resolution appears to be limited by the number and quality of the interference fringes detected by the camera.

\begin{figure}
  \centering
  \includegraphics{figures/simple-dhm/usaf-resolution}
  \caption{Reconstruction of a USAF 1951 Resolution target to establish resolution of the instrument. a) 1024$\times$1024 section of the hologram. b) Reconstruction of (a) at a distance of 3.92569~\si{\milli\meter}. c) 2048$\times$2048 section of the same hologram. d) Reconstruction of (c), also at 3.92569~\si{\milli\meter}. e) Intensity profile along a linear cross-section through group 7, showing that the lines in the first four elements are resolvable. This hologram was taken with 2.3 mW of laser power and $\sim$80~\si{\micro\second} exposure. Author's Note: In this figure and throughout this thesis I have placed scale bars on reconstructions but not on holograms. Holograms are not images in the traditional sense and scale bars give a false impression that one can make straightforward estimates of object size by inspection. }
  \label{fig:usaf-resolution}
\end{figure}

To investigate the effect of the camera resolution, we performed two reconstructions on the same hologram, one with a 1024$\times$1024 pixel subimage (shown in Figures~\ref{fig:usaf-resolution}a and b) and another with a 2048$\times$2048 subimage (shown in Figures~\ref{fig:usaf-resolution}c and d). In reconstructions based on the smaller subimage, group 6 element 3 is barely visible, giving a resolution of 6.2~\si{\micro\meter}.  When the larger field is reconstructed, group 7 element 4 is visible, giving a resolution of 2.76~\si{\micro\meter}.  This indicates that the camera can detect the high spatial frequency information outside the smaller subimage. Wavefront curvature does not appear to significantly affect the reconstructed image quality; the grid remains in focus throughout the field of view in the larger reconstruction.

The remainder of the information encoding spatial frequencies down to 1~\si{\micro\meter} is contained in fringes that either lie outside the reconstructed area or are too small, too blurry, or too faint to reconstruct accurately. This could be due to spherical aberration from the imaging optics, to nonuniform illumination or to the limited size and resolution of the sensor. Given the sharpness of the reconstructed images and our observation that the resolution is not significantly improved by higher numerical aperture objectives, we believe that the resolution is currently limited by the pixel density of the camera.  A recent professional-grade or a medium-format digital SLR camera, both of which are available commercially, may well be able to improve the instrument resolution at the same magnification.

To demonstrate the large depth of field made possible by holography, we image an $\sim200$~\si{\micro\meter} thick sample containing 2~\si{\micro\meter} sulfate latex spheres embedded in gelatin. Figure~\ref{fig:depth}a shows a hologram of this sample, and Figures~\ref{fig:depth}b and c show reconstructions at two different planes 160~\si{\micro\meter} apart. The white arrows indicate particles that are in focus at the two different planes; the instrument is able to capture both of them in the same hologram. Fig 3d shows a volume reconstruction of this sample.  The particles appear elongated due to an inherent effect of inline holography, as discussed by Sheng and coworkers~\cite{sheng_digital_2006}. This elongation increases for holograms of objects further from the focus of the objective. In our reconstructions the particles are elongated by a factor of about 20 at a distance of 3-4~\si{\milli\meter} from the focus of the objective, down to only a factor of 2 when near the focus. This variable elongation complicates quantitative axial measurements, but accurate transverse slices can still be obtained at any desired axial position.

\begin{figure}
  \centering
  \includegraphics{figures/simple-dhm/depth}
  \caption{Sulfate latex beads in gelatin slab of thickness $\sim200$~\si{\micro\meter}. a) Hologram. b) and c) Reconstruction at two planes separated by 160~\si{\micro\meter} (0.14~mm and 0.3~mm) in which different particles are visible.  White arrows show two different particles separated axially by 160~\si{\micro\meter} in the reconstructed image.  d) Isosurface volume reconstruction of this sample.  The particles do not appear spherical because of elongation induced by inline holography.  This hologram was taken with 0.235~mW of laser power and 20~ms exposure time.}
  \label{fig:depth}
\end{figure}

Finally, we demonstrate that the instrument can image live cells. Figure~\ref{fig:cells} shows a hologram and reconstructions of squamous epithelium cells. We show both amplitude and phase images reconstructed from a 2048$\times$2048 section of a hologram which contains 8 of these cells. Single cells can be visualized by zooming in on the reconstructed image. The nucleus is visible in both the amplitude and phase images, but the cell boundaries are clearer in the phase image. This is because the cell membrane and cytoplasm scatter weakly but are thick enough to affect the optical path length. Reconstruction at a different depth (Figure~\ref{fig:cells}f) shows a plane below the nucleus, demonstrating the ability to optically section. Some subcellular features are more visible in the amplitude image. Because both amplitude and phase images are available from the same hologram, one can choose the image that gives better contrast for the subcellular features of interest.

\begin{figure}
  \centering
  \includegraphics{figures/simple-dhm/cells}
  \caption{Squamous epithelium cells wet mounted and imaged approximately $f/2$ past the normal working distance of the objective. a) 2048$\times$2048 region of hologram. b) Amplitude image reconstructed from (a) at 3.998~mm. c) Phase image reconstructed at 3.998~mm. d) Close up of boxed region from (b), showing nucleus (dark) and outer edge of cell. e) Close up of boxed region from (c), showing nucleus and edge of cell in phase contrast. f) Close up of boxed region from (c) at 4.055~mm, showing a region below the nucleus. This hologram was taken with 2.3 mW of laser power and $\sim80$~\si{\micro\second} exposure.}
  \label{fig:cells}
\end{figure}


\section{Conclusions}
We have demonstrated a simple, inexpensive, self-contained holographic microscope capable of imaging unstained live cells with a depth of field greater than one hundred microns, a resolution better than 3 microns, and a total exposure of 200nJ per 3D reconstruction. We obtain sufficient contrast and resolution to identify single cells and subcellular features. For many applications, such a simple holographic microscope can replace a much larger and more expensive instrument, while at the same time offering unique advantages such as customized time sequences of exposures and quantitative phase contrast. Our results suggest that the current consumer-grade digital cameras may be able to bring the resolution of the microscope close to the diffraction limit.

But the possibilities for such a microscope go beyond simply replacing widefield or confocal microscopes. Portable and inexpensive microscopes can enable entirely new kinds of experiments. For example, holographic microscopy may be especially well suited for long duration imaging of living cell growth and organization. Ordinarily such experiments are done by placing an environmental chamber around a bulky microscope. A holographic microscope could be built inside a cell culture chamber, where it can follow movement in three dimensions without refocusing while at the same time subjecting the cells to minimal light flux. It could function autonomously over many days, a period that is generally infeasible with an expensive microscope and environmental chamber. The large depth of field and the ability to optically section samples may enable new studies of three-dimensional cultures, an important new direction in understanding tissue and tumor growth~\cite{pampaloni_third_2007}. Furthermore the short exposure time may allow the microscope to capture three-dimensional dynamics on much smaller time scales~\cite{lee_characterizing_2007, lee_holographic_2007} are possible in confocal microscopy.

Holographic microscopy has not yet caught on in biology.  We aim to lower the entry barrier for researchers without expertise in optics so that new experiments and new scientific discoveries become possible. To this end, the microscope we show here is only a first step; much remains to be done. In particular, the resolution needs to be improved to image smaller organelles and subcellular structures, the frame rate needs to increase, and reconstruction must happen in real-time. We believe that improvements in these areas will accompany the rapid evolution of consumer electronics.

\section*{Acknowledgments}
We thank Jose A. Dominguez-Caballero, Nick Loomis, George Barbastathis, Jeff Lichtman, and Stan Leibler for helpful discussions. This research was funded by the National Science Foundation under CAREER award number CBET-0747625. This material is based upon work supported under National Science Foundation Graduate Research Fellowships (TGD and EJG). DK and RM were supported by Department of Defense NDSEG Fellowships.
