1.1.

SI-Traceable Measurements

The use of SI units enables measurement results to be compared across more than a single device and across time. For FGI, this is beneficial for situations in which different devices and configurations may be used to assess the effectiveness of a particular contrast agent; examples include comparing two different imaging devices, evaluating components, or quantifying the impact of changing collection parameters. SI-traceable units allow for physically tractable comparisons of device characteristics.⁴ The process of converting counts to a radiometric unit requires calibrating the imager using SI-traceable artifacts. SI traceability is formally defined as the “property of the result of a measurement or the value of a standard whereby it can be related to stated references, usually national or international standards, through an unbroken chain of comparisons all having stated uncertainties.”⁵ The references may be physical standards such as optical sources and detectors or chemical standards, which are referred to as reference materials.⁶ Figure 1 is an illustration of the hierarchy of steps needed to go from an SI unit to standards used by the community. Each of these steps corresponds to a link in what is known as a traceability chain. At the top of this chain are the SI units based on universal physical constants, followed by the primary standard of a National Metrology Institute (NMI) used to physically realize the SI unit; secondary standards, which can be numerous, transfer the primary scale to reference instruments and artifacts that are then used to disseminate the standard unit to various communities for their scientific and commercial applications. There are often several steps in a traceability chain, and as illustrated by the width of the base of each step in the hierarchy, the uncertainty increases with each step away from the primary reference. Standards are created through consensus by a measurement community. The NMI works with measurement communities and facilitates the establishment of metrological traceability to the SI, as the latter guarantees comparability and universal acceptance of measurement results.⁷ In the USA, the National Institute of Standards and Technology (NIST) is the NMI.

Fig. 1

Illustration of the hierarchy of standards. The tissue phantoms can become a community standard.

1.2.

Fluorescence Imaging Tissue Phantoms

The specific function of the tissue phantom addressed in this paper is its use as a calibration optical radiation source to determine the response of a test imager to radiant flux in SI-traceable units. The FGI community has collectively produced various tissue phantoms for imaging system performance evaluation.^8–10 These physical constructs consist of a fluorescent material homogeneously mixed in varying proportions with absorbers and scatterers in a polymeric matrix to mimic fluorescence from tissues injected with a contrast agent.¹¹ The fluorophore in the tissue phantom is a more stable proxy of the contrast agent(s), which may not be shelf-stable or may not be able to be embedded in a solid matrix.¹² The fluorescence emitted from the surface, into free space, and collected by the imager is dependent on the optical characteristics of the tissue phantom material composition and the incident excitation radiation. The tissue phantom for establishing SI-traceability is a higher-order working standard and needs to have its emission be predictable. Often relatively simple in its physical construction, it needs to have a flat surface, be non-specular, and have easily measurable areal dimensions. This contrasts with functional tissue phantoms intended to mimic the shape of tissues and can be physically complex structures with a different set of performance evaluation goals.¹³ The sum of counts from all pixels $N_i$ attributed to the fluorescence, designated here as $S$, can be correlated with either the amount of fluorophore embedded in the tissue phantom, expressed in mole or kilogram, or the radiant flux from the tissue phantom, expressed in milliwatt or photons per second. The two are different physical quantities that can be made SI-traceable with different calibration routes. The first one requires calibration using the distribution of known amounts of material (SI-traceable to mole or kilogram) in the phantom, whereas the second requires a calibrated optical radiation source, heretofore referred to as source (SI-traceable to the optical watt). The fluorophore in the tissue phantom is itself a proxy for the contrast agent to be used in vivo, so it may not be a chemically significant substance; what is useful is when the relationship between its fluorescence output to that of the contrast agent of interest can be established. This concept of equivalency¹⁴ is used by the flow cytometry community in which there are many types of fluorophores used, sometimes even together in a single bead, and many devices to detect them. The community has successfully established measurement standards¹⁵ and a quantitation consortium.¹⁶

A single tissue phantom may be used to validate the performance of an imager intended for various contrast agents, and thus it is convenient to use the optical radiation-based calibration pathway, especially because optical radiation is a direct measurand of an imager. Both SI-traceability pathways will ultimately be needed to establish the response of an imager to a specific contrast agent. For the optical imager alone, its performance as a light collector can be evaluated using the tissue phantom as a calibrated source.

2.1.

Description of Calibration Procedure

The tissue phantom acquires its SI scale through comparison against a reference source. Because a reference source that matches the desired spectral band is not always available, one can be assembled and calibrated. The reference source needs to have an emission bandwidth less than the bandwidth of the FGI system for which the tissue phantom is designed. In practice, a narrowband source or a broadband source with a bandpass filter can be used. Figure 2 shows a diagram of the experimental setup of calibrating the tissue phantom against a reference source. The fluorescing tissue phantom (Quel Imaging, White River Junction, Vermont)^17,18 (A) is imaged using a low noise transfer camera (Pixis 1024BR, Princeton Instruments), (B) fitted with an 800 nm long-pass filter (FEL0800, Thorlabs), an example of a filter used for FGI, whereas the tissue phantom is irradiated with a collimated beam of 780-nm radiation from an LED (M780L3, Thorlabs), (C) at an angle of incidence of 25 deg. The excitation irradiance at the plane of the tissue phantom is measured using a calibrated photodiode¹⁹ (S2281-04, Hamamatsu), (D) that is swapped in place of the tissue phantom before its image collection. The tissue phantom is then removed after its fluorescence image is taken and replaced with an integrating sphere source (IS-3, Thorlabs), (E) which serves as the reference source, described below in Sec. 2.2. An image of its exit port is taken. Both images are later processed for analysis. The radiant flux at the image plane ${\mathrm{\Phi }}_{\text{image}}$ is a function of the radiance of the source $L_{\text{source}}$; the collection solid angle $\omega$, which is calculated as the ratio of the lens aperture area to the square of the distance from source to the lens aperture; and the area of the source $A_{\text{source}}$ [Eq. (1)]. The camera’s response to the radiant flux is reported in counts for all pixels that correspond to the source being imaged. The sum of counts ($N$) for all pixels attributable ($i$) to the source fluorescence is recorded as $S$ [Eq. (2)]. The imager’s responsivity in the specified spectral band, $R_f$, is the total counts $S$ generated in response to ${\mathrm{\Phi }}_{\text{image}}$ [Eq. (3)]

Fig. 2

Experimental setup in the calibration of a tissue phantom (A) against a reference source (E) using a transfer camera (B). Irradiance from the excitation radiation beam (C) is measured using a photodiode (D).

In this radiometric calibration, it is implicit that the response of the transfer camera to the radiant flux remains the same when the tissue phantom and reference source are measured sequentially, as long as the test and reference generate the same level of response, all collection parameters are the same, and the measurements are made as close in time as feasible. In other words, the transfer camera’s $R_f$ (test) is equal to $R_f$ (ref) during the calibration. A tissue phantom test source and a reference source are imaged using a transfer camera, one after the other, keeping all collection parameters the same. Using Eqs. (1) and (2) and rearranging terms, the radiance $L(\text{test})$ of the tissue phantom is determined.

2.2.

Test and Reference Source

The tissue phantom test source used in this example is a 3D-printed polymeric structure with 1000 nM concentration of IR-125 and unspecified absorptance and scattering properties. A 4-mm-diameter calibrated aperture is affixed in front of it to define the area. First, the imaging parameters are established (focus, $f$-stop, and distance). The tissue phantom is then irradiated with $<5\text{-}\mathrm{mW}$ excitation radiation to generate the fluorescence, and the irradiance level is recorded prior to collecting the tissue phantom image. After the tissue phantom image collection, an image of the reference source is then taken. The radiant flux from the tissue phantom surface is captured by the camera lens and relayed through the lens aperture at the given $f$-stop, forming an image of the source at the detector plane.

Figure 3 shows a diagram of a measurement station set up for measuring a dim test source such as a tissue phantom or other low radiance sources. The inset is the portion shown in Fig. 2. The reference source is the exit port of a 50.8 mm (2-in.) diameter integrating sphere onto which the same aperture used for the tissue phantom is affixed. Optical radiation from an 850 nm LED (F) (M850F2, Thorlabs) is split using a bifurcated optical fiber (TM50R2S1B, Thorlabs) (G, H), with a 90:10 split ratio. Output from the 90% branch (H) is measured using another calibrated photodiode (S2281-04, Hamamatsu) (I) as a monitor; output from the 10% branch (G) is input into the integrating sphere (E). This is an updated version of the measurement method described in Ref. 3, with additional redundancy in SI-traceability and expected lower measurement uncertainty. It is currently under internal performance validation and uncertainty budget development prior to availability for calibration service.

Fig. 3

LED source (F) emission is split using a bifurcated fiber with the 90% branch (H) going to a photodiode monitor (I) and the 10% branch (G) input into the integrating sphere (E), which serves as the reference source.

Specific steps are taken to minimize contributions to the measurement uncertainty budget. To minimize any detector nonlinearity effects, the LED source (F) drive current is adjusted until the average counts observed from the image of the reference source match that from the tissue phantom. No changes are made to the camera settings between the test and reference source measurements. All measurements of reference and test sources are made with the source normal to the transfer camera or test imager and centered along the optic axis. As with all radiometric measurements, alignment and dimensional measurements are major contributors to the measurement uncertainty.^20,21

2.3.

Tissue Phantom Calibration Value

For a given tissue phantom preparation (specific fluorophore, absorber, and scatterer concentration), the tissue phantom is calibrated for radiance $L({\lambda }_{\mathrm{em}})$ normalized to the excitation irradiance $E({\lambda }_{\mathrm{ex}})$ at a specified angle of incidence. The character $F$ is used here to express this ratio

2.4.

Example Calibration of a Tissue Phantom

In this example, the radiance of the test source (tissue phantom) is determined using Eq. (5). The reference source is calibrated using an NIST reference spectroradiometer²²

Table 2 shows an example of data from a tissue phantom radiance measurement against the reference source. $S$ is the sum of counts from all pixels in the image ($N_i$) attributable to the radiant flux at the image, ${\mathrm{\Phi }}_{\text{image}}$. The total counts are determined by drawing the circular regions of the images of the fluorescent sources using image processing software (ENVI, L3Harris Geospatial). Radiance of the same phantom affixed with a 4 and 5 mm aperture is shown in Table 2 along with the excitation irradiance used and the derived $F$ value. Using Eq. (1), ${\mathrm{\Phi }}_{\text{image}}$ is calculated. The solid angle $\omega$ is calculated using the area of the lens aperture (f1.4/23) at the $f$-stop used (f11; $A_{\text{lens apt}}$ is $0.034{\mathrm{cm}}^2$) and the distance from the sample to lens aperture (15.0 cm). The $R_f$ for the imager using radiance information is shown in the last column. This is the counts reported per mW of ${\mathrm{\Phi }}_{\text{image}}$ detected.

Table 2

Example data on a tissue phantom calibrated for radiance against a reference source. The same phantom is measured with a 4- and 5-mm diameter aperture.

Table 3

Illustration of how the calibration value F of the tissue phantom can be used to estimate signal changes.

2.5.

Use of the Imager Fluorescence Band Responsivity $R_f$

Changes to optical collection affect the imager signal. In this example, the now calibrated tissue phantom is imaged using the same camera at a different $f$-stop (5.6), at a different distance, at a different excitation irradiance, and on another day. The expected radiant flux and expected counts are calculated using the tissue phantom $F$ and the imager $R_f$ values (Table 3).

2.6.

Estimates of Uncertainty

Table 4 is a list of the successive steps in the determination of the $R_f$ of an imager using a tissue phantom calibrated for radiance. As shown in Fig. 1, each step in the calibration chain increases the measurement uncertainty. The procedure for the propagation of uncertainties according to Ref. 23 is followed.²³ Relative standard uncertainty $u$ of the measured quantity, expressed in % at coverage factor $k=1$, is generally used; expanded uncertainty $U$ at coverage factor $k=2$ is noted wherever it is used. Tables with a nonexhaustive list of the contributors to uncertainty for each of these steps are shown in the Appendix.

Table 4

Successive steps in determining Rf from a calibrated tissue phantom and the cumulative increase in its relative standard uncertainty.

2.7.

Choice of Imager Settings for Calibrating an Imager

It is beneficial to calibrate the imager at all anticipated configurations; parameters include exposure times, aperture settings, distances, and angles. This is important for systems in which the optical configuration can be changed during use, such as an imager with a zoom lens on an articulating arm, and corrections are needed. The following is an illustration of the effects of the choice of imager setting when determining $R_f$ of an imager.

It should be noted that the measurements in this section were performed prior to the tissue phantom calibrations described in the previous section, to explore whether it is feasible to do an imager responsivity calibration in situ using a portable source such as an LED source or a tissue phantom.

The $R_f$ of a camera (a second Pixis 1024BR, Princeton Instruments) is measured using a source (850 nm LED, Thorlabs) of known radiance. The camera was fitted with two different lenses and used at three different distances. Figure 4(a) shows the effect of exposure time on the measured $R_f$ value for different distances and lenses at the smallest aperture setting, as this allowed for long exposure times without saturation. In Fig. 4(a), the uncertainty bars shown ($U=8\%$ at $k=2$) are from the relative standard uncertainty of data collected at exposure times 0.2 s and longer. Short exposure times can lead to large uncertainties because the variability in the time that it takes the shutter to open and close becomes a significant proportion of the exposure time. Figure 4(b) shows the camera response at various aperture settings of the Schneider lens at 50.0-cm distance for 1.0-s exposure time, obtained using a linear fit of the acquired data at various exposure times, since a 1.0-s exposure time is not uniformly feasible at all aperture settings. The $R_f$ at larger apertures were lower than expected due to vignetting by an optical filter mount placed in front of the camera lens, and sensor saturation, both of which were verified by measurements. At the smallest aperture setting, the signal-to-noise ratio is low, increasing the uncertainty. At the largest aperture setting, stray light due to reflectance and scattering from surfaces near the lens edge and aberrations at the outer edges of the lens can affect the collected radiant flux in unexpected ways, also increasing the uncertainty. Thus, for Fig. 4(b), relative standard uncertainty using all eight aperture settings is $>30\%$ and reduces to 7% when only the middle five aperture settings are used. Table 5 summarizes the different optical configurations used to determine mean $R_f$, excluding the smallest and largest apertures.

Fig. 4

(a) The effect of exposure time on the imager response value taken at different distances with the smallest aperture for two lenses. (b) Larger aperture settings gave lower than predicted camera response due to vignetting by a filter mount installed in front of the lens and sensor saturation; these were subsequently verified by measurements.

Table 5

Measurement of mean Rf value across several different optical configurations using a calibrated radiance source.

This exercise shows that there are optimal settings at which to perform a calibration of the imager. In Fig. 5, the imager response $R_f$ at the three different sets of optical configurations from Table 5 is calculated using the radiance values from the calibrated source. For each test number, the $R_f$ is the mean value over measurements taken at various exposure times and over several $f$-stops. Using test data at all configurations shown in Table 5, the relative standard uncertainty in the mean $R_f$ value, $u(R_f)$, is 9%. This is shown in Fig. 5 with expanded uncertainty $U$ at 18% ($k=2$). The results were not corrected for the lens transmittance and likely account for the higher value measured with the Schneider lens, as it has a higher transmittance specification in the near-infrared region.

Fig. 5

Imager $R_f$ at three different optical configurations shown with $U(R_f)$ at 18% at ($k=2$).