2.1.

Experimental System

The system is depicted in Fig. 1 . A diode-pumped solid-state green laser with a $532\text{-}\mathrm{nm}$ wavelength (Laser Quantum) is used as the fluorochrome excitation source, $L_{\mathit{ex}}$ . The laser beam is spatially filtered and collimated using lenses, $L_1^{\prime }$ and $L_2^{\prime }$ , the pinhole, $P_1^{\prime }$ , and the diaphragm, $D$ , to form a relatively thin beam ( $1.5\text{-}\mathrm{mm}$ diameter, approximately). A pair of galvanometric scanners (GSI Lumonics, VM500), $G{S}_1^{\prime }$ and $G{S}_2^{\prime }$ (broken line), are placed in conjugate planes, which are also conjugated with the plane where the lens $L_7$ is placed, using for this purpose lenses $L_3^{\prime }$ to $L_6^{\prime }$ . The rotation axes of $G{S}_1^{\prime }$ and $G{S}_2^{\prime }$ are perpendicular and parallel, respectively, to the drawing plane of Fig. 1. In this configuration, when voltages are applied, the mirrors rotate, causing the beam to pivot around the optical axis at the plane of $L_7$ $(f=100\mathrm{mm})$ , generating an excitation source of approximately $50\mu \mathrm{m}$ diameter (assuming an Airy spot) in different positions on the surface of the object, $O$ , with embedded fluorochrome distribution, $FL$ . In Fig. 1, the beam is also conducted using the standard mirrors $M_1^{\prime }$ and $M_2^{\prime }$ and the dichroic mirror $DM$ (z532rdc from Chroma) which allows 1% of the green light reflected back by the object surface to pass through it. An additional orange He–Ne laser, $L_{\mathit{em}}$ , $594\text{-}\mathrm{nm}$ wavelength (Thorlabs), is spatially filtered and collimated to generate a beam that, contrary to the excitation laser, uses the maximum aperture allowed by the optical components. This beam passes through an electromechanical shutter, $S$ , and through a pellicle reflection beamsplitter, $BS$ (92% transmission–8% reflection). The light is then reflected by two additional galvanometric mirrors, $G{S}_1$ and $G{S}_2$ , in the same configuration described earlier, and passes with no significant absorption through the dichroic mirror, $DM$ , and lens $L_7$ to reach the object surface.

Fig. 1

Schematic drawing of the noncontact optical fluorescence tomography system.

The lens $L_6$ is placed on a motorized translation stage, $TS$ (Micos, PLS-85), to control the focus of the orange beam at a given point on the interface. The diffused light reflected from the surface forms an emission point source, whose light follows the reverse path to reach the sensor, a photomultiplier tube, $PMT$ (Electron Tubes, 9129B). In front of the sensor aperture, the lens $L_8$ conjugates—at the translation stage in-focus position—a $200\text{-}\mu \mathrm{m}$ -diam pinhole, $P_2$ , with the surface. A filter, $F$ (Chroma, HQ580/60m), is placed before the sensor with a passband of between $545\mathrm{nm}$ and $615\mathrm{nm}$ , which completely blocks the green laser. Taking into account the magnification of the optical system, $P_2$ scales to $170\mu \mathrm{m}$ diameter on the surface.

2.2.

Acquisition Procedure

The voltage generated by the $PMT$ was acquired using a high-speed $(100\mathrm{Ms}∕\mathrm{s})$ $8\text{-}\text{bit}$ resolution digitizer board (National Instruments, NI5112), and the control software was written in LabView, splitting the operation into two phases. First, two voltages are applied to the mirrors ( $G{S}_1$ and $G{S}_2$ ) according to a specific transversal point with coordinates $(y,z)$ ; then, a transistor-transistor logic (TTL) signal is sent to open the shutter, $S$ , and a relatively high voltage is sent to the mirror $G{S}_1^{\prime }$ thus deviating the excitation beam out of the path. In this state, the surface becomes illuminated only with light from the laser $L_{em}$ , and there is no fluorescence emission. In this configuration, the translation stage moves to find the displacement that maximizes the sensor signal. This position, which is directly related to a particular surface depth ( $x$ coordinate), brings the pinhole $P_2$ into focus with the surface by placing a virtual detector at the vector position ${\vec{r}}_i=(x,y,z)$ on the surface. In the second phase, the translation stage is maintained in the previously found position, the shutter $S$ closes, and registration of the fluorescence signal from the $PMT$ begins for the different voltages applied on the mirrors $G{S}_1^{\prime }$ and $G{S}_2^{\prime }$ associated to the excitation source vector ${\vec{r}}_k$ . This provides the data set, $J({\vec{r}}_i,{\vec{r}}_k)$ , which is suitable for tomographic reconstruction.³ Unlike in the acquisition subsystem, where the maximum allowed apertures are used to obtain information on maximum wave vector diversity, it is assumed that the beam diameter of the excitation laser is small enough to be always in focus on the surface, the $x$ coordinate obtained in the first phase serving to completely specify the ${\vec{r}}_k$ vector.

Although the previous procedure is suitable for obtaining a complete data set, the following results are obtained for dense registration using a small number of excitation positions. For this purpose, the software allows the process to be reversed: with $S$ open, a high voltage is applied to $G{S}_1^{\prime }$ to prevent fluorochrome excitation, and the voltages associated to the ${\vec{r}}_i$ detector position are sent to the mirrors $G{S}_1$ and $G{S}_2$ , initiating the focus search. Once concluded, two voltages are sent to the mirrors $G{S}_1^{\prime }$ and $G{S}_2^{\prime }$ to generate an excitation source at ${\vec{r}}_k$ , and the intensity of the fluorescent light is measured.

2.3.

Calibration

To test the system’s performance in terms of field of view, resolution, and range of focus that can be controlled, conventional intensity images of a chart were registered. For this, a flat squared regular mesh, obtained by printing black lines on white paper with $0.5\text{-}\mathrm{mm}$ pitch, was used and, to obtain images of the reflected light, a yellow LED was used to illuminate the target. Part of the LED spectrum was able to pass through the dichroic mirror and the filter, and so no modification of the optical system was needed, apart from including in the control the capability of switching the LED on and off when the shutter $S$ is closed or opened. Given that the surface is flat, to speed the process, a low-resolution image of $20\times 20$ points was first acquired and the surface information obtained was used to drive the translation stage for finer acquisitions.

Figure 2a shows the image obtained when the test is oriented perpendicular to the optical axis and the translation stage is fixed at the distance corresponding to the pixel on the optical axis. In this situation, the system is similar to a conventional digital camera, where the pinhole acts as a sensor element and the number of samples and the detector spacing are controllable by the voltages, while the field of view and the magnification depend on the maximum voltage and focal length of $L_7$ . With the available optics, we can use a maximum range of $\pm 0.4\mathrm{V}$ , producing a field of view of $0.668\mathrm{cm}$ . Although the illumination of the object was not even, the circular fading that can be seen in Fig. 1a is caused not by the illumination intensity distribution but by the limited apertures of the lenses between the galvanometric mirrors. Figure 2b shows the smearing of areas that become out of focus when the test is tilted. Figure 2c shows the image obtained when adapting the focus by moving the translation stage for each pixel. Panel (d) shows the same intensity values as in Fig. 2c, rendered as gray scaled dots placed in space in accordance with the encoded surface data. With the current optical system, we obtained a $0.3\text{-}\mathrm{cm}$ adjustable depth range. Figure 2c also shows a distortion in the image of the test due to a slight nonlinearity between the voltages applied to the mirrors and the transversal position coordinates.

Fig. 2

(a) Image acquired with the calibration test placed perpendicular to the optical axis. (b) Image obtained with the test tilted. (c) Image obtained with the test tilted and the translation stage moving. (d) The same intensity values as in (c) represented in three dimensions using the obtained surface information. The images have $60\times 60\text{pixels}$ , the units are millimeters, and the intensity has been normalized.

Note that the described focusing method results in variable acquisition numerical aperture and a disparity (depending on the axial coordinate) between the expected lateral surface coordinates addressed by the voltages and the real coordinates for the measured intensity for off-axis points. These two effects could induce artifacts in a tomographic reconstruction algorithm if the register data set is not modified accordingly before use. However, in the current system, they are not significant given the long focal length of $L_7$ compared with the depth variation and the field of view.

2.4.

Phantom

To test the system with fluorescence in a simulated biological medium, a solid cylindrical phantom,¹¹ shown in the central inset of Fig. 3, was fabricated. Isophthalic polyester resin and catalyst were mixed with India ink and titanium dioxide nano-powder (Sigma-Aldrich) before curing in adequate quantities to simulate scattering and absorption of approximately ${\mu }_s^{\prime }=8{\mathrm{cm}}^1$ and ${\mu }_a=1.4{\mathrm{cm}}^1$ . To better evaluate the performance without restricting the generality of the method, instead of using a complicated surface, one of the flat surfaces of the phantom was used as simulated air/tissue interface.

Fig. 3

The central inset is a drawing of the solid phantom $(1\mathrm{cm}\text{diameter}\times 3\mathrm{cm}\text{length})$ showing a $1\text{-}\mathrm{mm}$ -dim drilled hollow column filled with fluorochrome. The boxed area corresponds to the excitation/acquisition window used. (a) The interface surface in this configuration is oriented perpendicular to the excitation beam (arrow). (b) The interface surface is oriented at a given angle to the incident excitation beam (arrow). Each point in the plane represents an acquisition point. In the cylinder, the points represent positions of the fluorescence sources used to simulate the emission through the interface surface. Units in (a) and (b) are mm.

A cylindrical hollow—also shown on the central inset of Fig. 3—of $1\mathrm{mm}$ diameter was drilled centered approximately $1.5\mathrm{mm}$ from the interface surface and filled with a water solution of Alexa A538 (Invitrogen) in the form of goat anti-mouse IgG $(\mathrm{H}+\mathrm{L})$ with a concentration of $0.2\mathrm{mg}∕\mathrm{ml}$ .

A548 fluorochrome was chosen to demonstrate the operation of the system using the lasers and sensor available in the laboratory. The $532\text{-}\mathrm{nm}$ laser is able to excite the fluorescence with a quantum efficiency of around 40%, obtaining emission at $603\mathrm{nm}$ , close to the He-Ne laser orange wavelength. The dichroic mirror and filter combination is suitable for these excitation/fluorescence wavelengths and also allows the He-Ne laser light to pass through them.

3.1.

Acquired Data in an Unbounded Infinite Medium

The first experiment consisted of registering images of the phantom surface with fluorescence light for several excitation points. The data was obtained acquiring $0.5\mathrm{Ms}$ of the $PMT$ output voltage. Given that the scanners have a limited bandwidth of around $3\mathrm{kHz}$ , the preceding parameter determines the total acquisition time. We limited the sampling to $60\times 60\text{pixels}$ and $\pm 0.2\mathrm{V}$ voltage range for the mirrors $G{S}_1$ and $G{S}_2$ corresponding to a window of $3.34\mathrm{mm}\times 3.34\mathrm{mm}$ . This area is represented as the shaded square in the central inset of Fig. 3.

In a first experiment, the phantom was placed with its flat surface closest to the fluorochrome column and perpendicular to the excitation beam that follows the direction of the arrow shown in Fig. 3a [zero voltage applied to mirrors $G{S}_1^{\prime }$ and $G{S}_2^{\prime }$ or ${\vec{r}}_{\mathit{exc}}=(0,0,0)$ ]. After placing the phantom, the system was automatically focused by running the focus search mechanism. Figure 4a, shows the image obtained on the left, together with the excitation spot on the interface surface on the right, which was obtained by removing, after fluorescence acquisition, the filter $F$ and reducing the sensitivity of the $PMT$ by limiting the number of acquired voltage samples per pixel from $0.5\mathrm{Ms}$ to $0.05\mathrm{Ms}$ . Note that the system generates an image of the excitation spot extended by its convolution with the scaled detection pinhole on the surface.

Fig. 4

(a) Fluorescence distribution (in the left panel) for the phantom placed as shown in Fig. 3a and the excitation spot (in the right panel); (b) the data transformed using Eq. 1; (c) the corresponding simulated distribution; (d) the fluorescence image (on the left) for a displaced excitation spot (image on the right); (e) the previous data after the use of Eq. 1; (f) the corresponding simulated image; (g) fluorescence image obtained for the phantom placed as shown in Fig. 3b; (h) the data obtained with the translation stage static; (i) the result of Eq. 1 applied to the data represented in panel (g); (j) the corresponding simulated data.

In order to compare the fluorescence intensity distribution with that theoretically expected, the acquired data on the surface, $J({\vec{r}}_i,{\vec{r}}_k)$ was transformed to a new data set corresponding to what would be acquired by the same excitation source and detector spatial distribution but in an unbounded medium, $U^{\mathit{inf}}({\vec{r}}_i,{\vec{r}}_{\mathit{exc}})$ , using the formula¹²

Figure 4b shows a window of $30\times 30$ centered pixels resulting from the calculation specified by Eq. 1 and carried out using the complete $60\times 60$ registered intensity data of Fig. 4a. This clipped window discards the representation of pixels with inconsistent values caused by the border effect inherent in the squared truncation of the data due to the limited sampling area. Figure 4d on the left shows the fluorescence intensity distribution for the excitation spot on the surface shown on the right $[{\vec{r}}_{\mathit{exc}}=(0,-0.05,0)]$ . Panel (e) in Fig. 4 shows the result of Eq. 1 applied to the fluorescence data.

The image in panel (a) of Fig. 4 shows a structure in the form of a notch. This corresponds to similar features in the phantom surface that were observed by inspection using conventional illumination in reflection and was caused by the surface cutting. The emergence of these features in the fluorescence images is not due to absorption but corresponds to deficits in the flux after traversing the surface due to the presence in the light of high spatial frequencies—generated by surface irregularities in the fluorescence light traversing the interface—above the cutoff frequency of the optical acquisition system limited by the numerical aperture (NA) 0.13 of $L_7$ . Although these structures are artifacts in the reconstruction data set, their observation in focus means that the surface is correctly conjugated onto the detector plane.

Another characteristic in the data is the presence of autofluorescence arising in the form of a circular spot centered at the excitation location. This can be more clearly seen in the right image of panel (d) in Fig. 4. Discarding the other components used to fabricate the phantom, the autofluorescence term in the intensity is generated close to the surface by the resin.

In a second experiment, the excitation point ${\vec{r}}_{\mathit{exc}}=(0,0,0)$ was again used, decreasing the laser power to reduce the autofluorescence component in the signal, whereas the surface was tilted as shown in Fig. 3b. In this case, the translation stage moves for each position associated to each pixel before acquisition of the fluorescence intensity, encoding the surface in the process. Figure 3b shows the fitted plane obtained from the data. Figure 4g shows the intensity distribution obtained, while panel (i) shows the result using Eq. 1.

Figure 4h shows the acquired image for this excitation coordinate when, after adjusting the focus for the detector position $\vec{r}=(0,0,0)$ , the translation stage remains static during registration at the other transversal detector coordinates. Equation 1 was used and the result compared with the intensity distribution represented in Fig. 4i. Figure 5 shows the pixel values along a horizontal cut at the center of both images, demonstrating that the first effect of defocusing the surface points (other than those close to the central vertical axis) is a weaker signal.

Fig. 5

Comparison between the horizontal normalized intensity profiles versus pixel values when the pinhole is dynamically conjugated with the surface for the different acquisition points (solid line) and when the pinhole remains conjugated only with the central acquisition point (dotted line).

3.2.

Comparing the Acquired Data with the Numerical Simulation

In an infinite medium, assuming a uniform discretized fluorochrome distribution $\varphi \left({\vec{r}}_j\right)$ inside a given voxelated volume, $V$ , within a uniform scattering and absorption coefficient limited by a surface $S$ , the average intensity at point ${\vec{r}}_i$ due to a point static excitation source at ${\vec{r}}_{\mathit{exc}}$ is given by¹³

In the phantom, $\varphi \left({\vec{r}}_j\right)$ represent a cylindrical distribution, whose orientation and exact position with respect to the optical axis is approximately known since it is manually placed. Equation 2 allows quantitative comparison of the experimental data—once transformed by Eq. 1—and the expected intensity distribution.

Figures 4c and 4f shows the result of the simulation using Eq. 2 when the phantom is placed as in Fig. 3a for excitation sources at ${\vec{r}}_{\mathit{exc}}=(0,0,0)$ and ${\vec{r}}_{\mathit{exc}}=(0,-0.05,0)$ , respectively. Only relatively low intensity values of the image in panel (c) can be compared with pixels of low intensity in (b) since the original data [Fig. 4a] contain information of fluorescence together with autofluorescence for the central pixels. Some distortion is caused by the lack of information on the fluorescence intensity caused by the surface notch. The intensity distribution in panel (e) of Fig. 4 is comparable with the simulated intensity distribution of panel (f), after discounting the distortion in the elliptical shape that the autofluorescence peak causes. The image in panel (j) corresponds to the intensity distribution expected for the configuration shown in Fig. 3b and excitation at ${\vec{r}}_{\mathit{exc}}=(0,0,0)$ . Again, to discard the autofluorescence, when comparing with the image of panel (i) corresponding to the data obtained from the same phantom position, only pixels distant enough from the image center can be considered, showing the elliptical shape predicted by the simulation.

As a final example, Fig. 6a shows a window of $15\times 15\text{pixels}$ of the data set computed using Eq. 1 from the $30\times 30$ surface virtual detectors and surface data when the phantom is placed as in Fig. 3b using the previous acquisition voltage range and several excitation points. In this case, the pixel size is better matched with the diameter of detection pinhole on the surface. In the horizontal direction, the excitation coordinates for which the data are shown correspond approximately to the system fluorescence signal detection limit. Figure 6b shows the simulation results using Eq. 2 for the same excitation points. The reason for these images appearing noisier than the image in Fig. 4i is not due to a different excitation intensity but to the use of fewer values in the sum of Eq. 1 and the lower degree of filtering resulting from convolution with the detection pinhole in the registered data. Despite the autofluorescence component in the signal, it can be affirmed that the registered data follow the expected fluorescence intensity distribution.

Fig. 6

(a) Fluorescence data of virtual detectors placed in the interface surface for different excitation coordinates of the phantom of Fig. 3b. (b) Simulated data using Eq. 2. The $15\times 15\text{pixels}$ images are normalized using the ensemble maximum and minimum values.