LED-based integrating sphere light sources (LED-ISLSs) in the size of typical microscope slides were developed to calibrate the radiance responsivity of optical imaging microscopes. Each LED-ISLS consists of a miniaturized integrating sphere with a diameter of 4 mm, an LED chip integrated on a printed circuit board, and a thin circular aperture with a diameter of 1 mm as the exit port. The non-uniformity of the radiant exitance of the LED-ISLSs was evaluated to be 0.8%. The normal radiance of the LED-ISLSs in the range of (5∼69) W m−2 sr−1 was measured with a standard uncertainty of 1.3% using two precision apertures and a standard silicon photodetector whose spectral responsivity is traceable to an absolute cryogenic radiometer. The LED-ISLSs were applied to calibrate the radiance responsivity of a home-built optical imaging microscope with a standard uncertainty of 2.6∼2.9%. The LED-ISLSs offer a practical way to calibrate the radiance responsivity of various optical imaging microscopes for results comparison and information exchange.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
Fluorescence microscopy has been widely applied in the frontiers of many research fields such as biomedical analyses and an enormous amount of effort has been devoted to the development of more advanced fluorescence microscopy technologies . For instance, multi-photon microscopy has been applied in deep tissue imaging and visualization [2,3], neural activity monitoring  and real-time cancer diagnosis ; total internal reflection fluorescence microscopy has been widely used in the investigation of cell dynamics, such as endocytosis , exocytosis  and cell adhesion ; light sheet-based fluorescence microscopy, particularly suitable to analyze live mammalian cells, was applied to study the formation of cellular spheroids with long periods  and high resolution ; furthermore, stimulated emission depletion fluorescence microscopy was used to deliver diffraction-unlimited images of biological molecules, such as immunostained microtubules , vesicle membrane protein synaptotagmin I , and Bruchpilot protein .
Among the biomedical applications of fluorescence microscopy, a significant part of the applications require quantitative analysis of the results. The measurements of fluorescence intensity and concentration of the labeled target is one of the categories of quantitative analysis of fluorescence microscopy. For instance, by measuring the fluorescence intensity of a DNA probe, the DNA content per cell was determined . Another category of quantitative analysis is the ratio measurement based on the fluorescence intensity. For instance, some fluorescent dyes respond to Ca2+ or H+ concentrations by changing the fluorescence intensity at different wavelengths, thus the ratio of fluorescence intensity at two wavelengths was able to reveal the concentration information of the ions . Furthermore, dimensional measurements of the fluorescence microscopy, including 2D and 3D, are also of great importance in quantitative analysis of fluorescence microscopy. A cutting-edge application for fluorescence microscopy dimensional measurement is the use of fluorescence resonance energy transfer for molecular geometry measurement at the nanometer scale [16,17]. Summarizing the applications of quantitative fluorescence microscopy, two key components of the fluorescence microscopy image data are dealt with: image pixel intensity, and image pixel size . Fluorescence image data from different setups, or different research groups usually need to share with results comparison and information exchange. Therefore, two types of calibration are needed for quantitative analysis of fluorescence microscopy, namely, geometric (or size) calibration, and radiometric (or intensity) calibration.
Geometric calibration is needed when image sizes are compared from different microscope configurations. For example, in cytometry the cell sizes are estimated from the fluorescence image pixel size . To compare the cell size results obtained from different cytometrical microscopes, the calibration of true geometric scale of the image pixel size is needed. Several methods are available for geometric calibration, such as nanobead/microbead-based NIST traceable particle size standard , standard fluorescent patterns from distributed nanoparticles embedded in glass-substrate slides [21,22], laser-written fluorescent patterns , DNA-origami rulers , and etc.
Radiometric calibration is required when the fluorescence intensity or image pixel intensity are compared between optical imaging microscopes in different configurations. For example, cytometric analysis allows the estimation of cell numbers by measuring the fluorescence intensity of the fluorophore label . Due to the plurality choices of microscope components with distinct optical properties such as the spectral responsivities of detectors, the linearity of the detector responsivity, the field of view of the imaging microscope, optical throughput of objective lens , and so on, the comparison of results from different optical imaging microscopes are only meaningful after a rigorous radiometric calibration of each microscope. Various methods have been proposed by researchers for such a purpose. Standard fluorescent beads are widely used for radiometric calibration in flow cytometry [26–28]. Fluorescent layers embedded in microscope glass-slides are also used to create a uniform radiance field under laser excitation [29–33]. The excitation laser intensity on the illuminated surface needs to be excessive or should be accurately measured to quantify the photoemission efficiency. Another category of radiometric calibration method adopts self-luminous standard radiance sources, such as LED-based sources. Slide-based planarly distributed LED beads [34,35], and LED-illuminated thin-film transistor liquid-crystal display modules  have been developed as a stable radiance source for the radiance responsivity calibration of optical imaging microscopes. Ideally, a radiance responsivity calibration source should have such characteristics: 1) temporally stable and spatially uniform radiance, 2) compatible light intensity and wavelength range, 3) compact size for easy manufacturing and implementation, and 4) traceability to SI. Research efforts are underway in pursuit of simple, stable, accurate, and cost-effective standard calibration sources for radiometric calibration of optical imaging microscopes.
In this work, we demonstrate a series of miniaturized LED-based integrating sphere light sources (LED-ISLSs) which can be employed as standard radiance sources for the radiance responsivity calibration of optical imaging microscopes. The design and fabrication, the radiometric characterization, the calibration, and the applications of the LED-ISLSs is explained in detail. The results show that the LED-ISLSs may be an effective solution for the radiance responsivity calibration of optical imaging microscopes and will help comparisons of the results obtained from different systems.
2. Design of the LED-ISLSs
Each of the LED-ISLSs was constructed via a multilayer assembly scheme, consisting of four different layers as illustrated in Fig. 1(a):
The substrate layer (Layer 1) is a printed circuit board with a super thin LED chip (Vishay Semiconductors, VLM series), an electronic circuit to provide 4-level DC forward current, and a 3.7-V lithium-ion battery power pack. Four different color LEDs in a size of 1.0×0.5×0.35 mm3 were implemented at around the center of Layer 1, as shown in Fig. 1(b). The maximum level of DC forward current was 20 mA for red and orange LEDs based on AlInGaP materials and 5 mA for green and blue LEDs based on InGaN materials.
The second and third layers (Layer 2 and Layer 3, respectively) form two hemispheres of a miniaturized integrating sphere with an inner diameter of 4 mm. Both layers were made of a PTFE-based semi-transparent plastic material with 0.85 diffuse reflectance and 0.15 diffuse transmittance in the visible range. The miniaturized integrating sphere was positioned right above the LED mounted on Layer 1 and illuminated by the diffusely transmitted light through Layer 2. The light was homogenized in the miniaturized integrating sphere and exits from a circular port with a diameter of 1.5 mm on top of Layer 3.
The cover layer (Layer 4) was a piece of thin aluminum plate with an anodized black front surface. A circular aperture with a thin edge was machined in Layer 4 right above the exit port of the integrating sphere. The diameter of the aperture was measured to be 1.002 mm by comparing the radiant power through it to that through a standard 4-mm-diamter aperture in a highly uniform irradiance field. Note that the back reflection from Layer 4 may deteriorate the uniformity of the light diffusely transmitted through Layer 2 without adoption of Layer 3.
The four layers were assembled to achieve a slide-shape LED-ISLS, as shown in Fig. 1(c)-(d), in a size of 75×25×9 mm3, which is the size of a typical commercial microscope slide. The LED-ISLSs can be then well adapted for the radiance responsivity calibration of a variety of optical imaging microscopes.
3. Optical properties of the LED-ISLSs
3.1 Spectral characteristics
The spectral characteristics of four different types of LED-ISLSs were examined using a compact (200-1000) nm spectrometer (Thorlabs CCS200). The relative spectral radiance responsivity of the fiber spectrometer was calibrated using a reference lamp (Halogen-Tungsten lamp) and a reference diffuser plate. The peak wavelength, full-width-half-magnitude (FWHM), and relative power spectral density distribution from the exit port of each LED-ISLS were measured and the results were as follows: the peak wavelengths were 468 nm, 519 nm, 595 nm, and 644 nm, respectively; the FWHMs were 22.9 nm, 26.2 nm, 13.3 nm, and 15.1 nm, respectively; the relative spectral power density distribution of each LED-ISLS was calculated by normalizing the spectral intensity at each wavelength to the integrated intensity in the full spectral band, as shown in Fig. 2. The relative spectral power density distribution is important to calculate the spectrally-integrated radiance of each LED-ISLS, which will be explained in detail in Section 3.4.
3.2 Temporal stability
The working current of each LED-ISLS can be set at 4 different levels (from Level 1 to Level 4), corresponding to 25%, 50%, 75%, 100% of the maximum level of DC forward current, respectively. The temporal intensity stability of each LED-ISLS was evaluated based on the results of 70 consecutive measurements on each LED-ISLS over a time span of 7 minutes. The relative standard deviations (RSDs) of the LED-ISLSs at 4 different intensity levels were analyzed as follows: for the blue LED-ISLS, the RSDs from Level 1 to Level 4 were 0.906%, 0.89%, 0.382%, and 0.365%, respectively; for the green LED-ISLS, the RSDs from Level 1 to Level 4 were 1.562%, 0.561%, 0.91%, and 0.337%, respectively; for the orange LED-ISLS, the RSDs from Level 1 to Level 4 were 0.633%, 0.695%, 0.519%, and 0.511%, respectively; for the red LED-ISLS, the RSDs from Level 1 to Level 4 were 1.098%, 1.289%, 1.033%, and 0.439%, respectively. The normalized measurement results of the four different color LED-ISLSs at Level 4 were illustrated in Fig. 3. The temporal stability is generally low when the working current is small, indicating that more effective methods than simply lowering the working current may be required to reduce the intensity of the LED-ISLSs with good temporal stability. Long-term stability of the LED-ISLSs was also checked. After ageing for 120 hours, the relative deviation of the average radiance of the LED-ISLSs during a period of 420 s was about 0.2%. Better temporal stability might be achieved via better thermal management.
3.3 Non-uniformity of radiant exitance
To evaluate the non-uniformity of radiant exitance at the LED-ISLS exit port, we built a home-made microscope which consisted of an objective lens (Olympus PLN 10×) and a scientific CCD camera (Thorlabs, 340M-USB). The objective lens had a numerical aperture (NA) of 0.25. The LED-ISLS was placed on a three-dimensional translation stage, with the exit port facing the objective lens. A small aperture with 1 mm diameter was placed in front of the CCD image sensor to limit the image of the aperture of the source, as shown in Fig. 4(a). A small area from the exit port of LED-ISLS was imaged on the CCD image sensor (Fig. 4(b)). The blurry edge resulted from the imperfect modulation transfer function of the imaging system. The red circle in Fig. 4(b) was the area used for analysis. By moving the LED-ISLS in the same plane of the exit port, radiant exitance from different small areas of the exit port was collected by the objective lens and subsequently imaged on the CCD image sensor. The moving step distance was 0.05 mm. The average pixel intensity of the analyzed area at each scanning position was calculated. The normalized pixel intensity distribution across the exit port is shown in the left of Fig. 4(c). The data at the edge of the exit port were omitted because the view of the small aperture was not fully filled by the radiant exitance at the edge. Using an image of a grid ruler at the same position of the LED-ISLS exit port, the actual magnification factor of the microscope was measured to be 11.05. The total imaging area of the CCD was 4.736×3.552 mm2. The observed area from the exit port by the microscope was then estimated, showing in the red rectangular box of Fig. 4(c). Note that the vertical marginal 100 pixels and horizontal marginal 50 pixels were excluded, which will be explained in Section 5. From Fig. 4, the non-uniformity of the radiant exitance from the observed area was estimated to be ∼0.8%.
The normalized pixel intensity distribution in Fig. 4(c) was also used to correct the radiant exitance of a specified area. The ratio of radiant exitance from a specified area A on the exit port to the radiant exitance from the entire exit port, f1(A), is:
3.4 Spatial distribution of radiance
A scan detector was assembled using a thin-edge aperture with a 1-mm diameter mounted in front of an integrating sphere photodetector to evaluate the spatial distribution of the radiance of the LED-ISLS. The measurement scheme is illustrated in Fig. 5(a). The scan detector can be moved in a x-y plane parallel to the cover layer of LED-ISLSs and the distance between the aperture of the scan detector and the exit port of the LED-ISLS was 35.1 mm. The responsivity of the integrating sphere photodetector is insensitive to the angle of the incident radiant flux. The spatial distribution in the x-y plane of the radiant flux from each LED-ISLS was measured with a scanning resolution of 2 mm and the relative radiance can be calculated based on the radiant flux and geometric characteristics. A typical spatial distribution of the radiance of an LED-ISLS is highlighted in Fig. 5(b). Ideally, for a perfect Lambertian source, the radiance of the source should be nearly the same for a wide solid angle. However, the radiance calculated from the radiant flux detected by the scan detector at each scanning position (x, y), denoted as Φx,y, keeps decreasing from the center of the scanning plane towards the edge after corrections using cosine-fourth-power law . Here we used the cosine-fourth-power law to check how much our source deviated from an ideal Lambertian source. From Fig. 5(b), the ratio of average radiance from the entire exit port within the extended solid angle Ω (or the corresponding NA of an objective lens) to the average radiance from the entire exit port at normal direction f2(Ω) (or f2(NA)) was estimated, as shown in Fig. 5(c):
3.5 Radiance measurement
Radiometrically, using two apertures to confine the field-of-view, one can calculate the transfer of radiance between the source and the detector [38,39]. This detector-based method for radiance measurement was also previously demonstrated using a spectrally resolved integrating sphere light source to calibrate detector spectral radiance responsivity in our lab . The spectral responsivity of a standard photodetector based on a silicon photodiode (Hamamatsu, S1337) was traceable to the national primary standard (for instance, an absolute cryogenic radiometer in National Institute of Metrology, China [41,42]).
In this work, the two-apertures system was used to measure the radiance of the LED-ISLS, as shown in Fig. 6(a). The exit port of the LED-ISLS (1 mm diameter aperture with thin edge) was used as the precision aperture for the source, of which the area was denoted as AS; a precision aperture with a 4-mm diameter was placed closely in front of a standard photodetector based on a silicon photodiode as the precision aperture for the detector, of which the area was denoted as AD, defining the effective detection area. The distance between two apertures d was measured to be 69.02 mm. The solid angle of the source extended to the detector was calculated to be Ω = AS/d2. The total incident radiant flux, ΦS,N, on the effective detector area is:
Based on the relative power spectral density distribution s(λ) (calculated from results shown in Fig. 2) and spectral responsivity of the silicon photodetector R(λ) (calibrated by absolute cryogenic radiometer, in the unit of A/W), the total incident flux received by the silicon photodetector can be derived as:7. LS, N was measured to be in the range of 5 to 69 W m−2 sr−1. LS, N can be used to calculate the average radiance entering the microscope objective lens, which will be explained in the next section.
4. Radiance responsivity calibration for optical imaging microscopes
The radiance-calibrated LED-ISLS was applied to calibrate the radiance responsivity of a home-built optical microscope, as shown in Fig. 5(b). The setup was the same as the one used for radiant exitance non-uniformity measurement in Section 3.3, except that the 1-mm small aperture was removed here. To calibrate the radiance responsivity of the microscope, the edge of the exit port was firstly focalized and imaged on the CCD camera by moving the translation stage, then the center of the exit port was parallelly moved in to fill the entire CCD image sensor. Images from 4 colors and 4 radiance levels were taken and the radiance responsivities were evaluated. Figure 7(a) shows an example of the CCD images from the illumination of the LED-ISLS in blue color at 4 radiance levels.
The radiance responsivity of the microscope, RL, can be defined as:
Photoelectrons generated as incident photons are received in the depletion region of the metal oxide semiconductor of the CCD, and subsequently measured by an analog-to-digital converter (ADC) to indicate the incident light flux. The CCD contains a 14-bits ADC, which offers 214=16384 gray levels, as the analog-to-digital units, or “counts”, displayed on the digital image. The read noise is about 15 photoelectrons for each pixel at 20-MHz readout rate. To fully use the dynamic range of the CCD, an ADC gain was set for each color and radiance. The photoelectron rate of each pixel, φ, (in the unit of s−1) was calculated as:
The calculation of the average radiance entering the microscope objective lens LO must take into consideration the non-uniformity of radiant exitance evaluated in Section 3.3 and the radiance spatial distribution evaluated in Section 3.4. From Fig. 4(c) and Eq. (1), the radiance of the observed area from the microscope at normal direction, LO, N can be calculated from the average radiance at normal direction (Eq. (6)):4(c)) at normal direction to the average radiance from the entire exit port of LED-ISLS at normal direction, calculated from Eq. (1). From Section 3.4, the radiance entering the microscope objective lens is a weighted average radiance, which can be corrected by Fig. 5(c) and Eq. (2) or Eq. (3). Using the NA value given by the objective lens manufacturer (NA=0.25), the radiance from the observed area entering the microscope objective lens LO is then calculated as: 5(c) and Eq. (3).
Finally, the average radiance entering the microscope objective lens LO has an expression as:7.
The average photoelectron rates versus average radiance entering the microscope objective lens are shown in Fig. 8(b). Good linearity of camera response from four different radiance levels was obtained. The radiance responsivities of the microscope at different colors, RL, are summarized in Table 1. Note that the radiance responsivity is wavelength dependent, as it is a product of the quantum efficiency of the camera, the spectral transmittance of the objective lens and the camera window.
One might raise the question of the rationality of using the radiance responsivity RL to evaluate the characteristic of microscope responsivity. Another important parameter to evaluate the characteristic of microscope responsivity is the microscope quantum efficiency, ηM expressed as:
5.1 Non-uniformity of the pixel radiance responsivity
The non-uniformity of the pixel radiance responsivity of an optical imaging microscope can be evaluated by comparing the photoelectron rates of the pixels on the CCD sensor. In order to avoid the unfavorable marginal effects on the CCD sensor caused by the scattering effect of the optics or the readout scheme of the electronics, the vertically marginal 100 pixels and horizontally marginal 50 pixels were excluded for the non-uniformity analysis (Fig. 9(a)). Then the relative pixel photoelectron rates were examined for the cropped image (Fig. 9(b)). The histogram of the calculated relative deviations for the pixels was illustrated in Fig. 9(c). The statistical result followed a Gaussian distribution with a standard deviation of ∼1%.
The non-uniformity of the pixel radiance responsivity may have resulted from the non-uniformity of the radiant exitance of the LED-ISLSs, the light collection efficiency and throughput of the imaging optics, and the quantum efficiency of the CCD sensor. Previously, we have demonstrated the non-uniformity of the radiant exitance of the effectively observed area from LED-ISLSs was about 0.8% in Section 3.3.
For a 10× objective lens with an NA of 0.25 used in the optical imaging microscope, we can estimate the non-uniformity of the light collection efficiency and throughput of the imaging optics. For a point within the effective area with a size of 0.363 mm × 0.188 mm on the exit port of the LED-ISLSs imaged onto the CCD sensor, the effective light collection solid angle of the objective lens is almost the same as that for the central point of the imaged area. However, the objective lens collects the light in a projected area with a displacement off the center on the spatial distribution map of the radiance of LED-ISLSs as studied in Section 3.4 (Fig. 10(a)). The difference of the collected light intensity can be estimated to have a deviation of <0.2% for any point within the imaged area (Fig. 10(b)). The light emitted from different points in the imaged area goes through different optical paths in the objective lens, and therefore the non-uniformity of the throughput of the imaging optics needs to be examined. For an optical imaging microscope using an objective lens with a much higher NA, the analysis of the non-uniformity of the light collection efficiency and throughput of the optics is similar. However, the calculation of the average radiance collected by the microscope becomes more difficult with a larger uncertainty since the radiance decreases significantly off the center of the exit port of the LED-ISLSs.
The non-uniformity of the quantum efficiency of each pixel of the CCD sensor may be precisely measured using a highly uniform irradiance field covering at least one single pixel and scanning over the CCD sensor. The non-uniformity of a CCD sensor normally can be in the range of a few tenths to a few percent.
The method of scanning a pinhole light source can be used to study the non-uniformity of pixel radiance responsivity of an optical imaging microscope. However, the method is limited to the evaluation of the non-uniformity but not suitable for the absolute calibration of the radiance responsivity of the optical imaging microscope. One of the key issues is that, the area of the pinhole is difficult to be manufactured and characterized with high precision.
5.2 Uncertainty analysis
The uncertainty of the radiance of the LED-ISLSs was analyzed and summarized in Table 2. Type B uncertainty sources include the spectral responsivity of the Si standard photodetector, the interpolation of the spectral responsivity, the relative spectral radiance responsivity of the spectroradiometer, the interpolation of the relative spectral radiance responsivity, the area of the precision aperture in front of the Si photodiode, the area of the aperture as the exit port of the LED-ISLSs, and the distance between the two apertures. Type A uncertainty sources include the temporal stability, spatial uniformity, as well as the measurement repeatability of the output of the LED-ISLSs. The combined standard uncertainty can then be evaluated to be 1.3%.
The uncertainty of the radiance responsivity of the optical imaging microscope can then be evaluated based on the results of the LED-ISLSs. The key components for the radiance responsivity calibration are the uncertainty of the normal radiance of the source (∼1.3%), the uncertainty of f2(NA) resulted from the NA measurement uncertainty (∼1.2%), the camera radiance responsivity nonuniformity (∼1%), and the linear fitting uncertainty (1.68∼2.06%). The combined standard uncertainty for the home-built optical imaging microscope can be analyzed to be 2.6∼2.9%.
The advantages of the LED-ISLSs designed in this work are evident. First, all the necessary components have been incorporated into a box with a size of a standard glass slide allowing quick implementation on the sample stage of any standard optical imaging microscopes. Secondly, the LED-ISLSs have very low power consumption and work for a long time using a thin rechargeable lithium battery pack; the thermal management of the chip LEDs is simple and the temporal stability of the light intensity is good over the long working period. Thirdly, the emission spectrum of an LED-ISLS can be blended using different LEDs selected from a wide range of peak wavelengths and colors; one or multiple laser diodes with narrow emission wavelengths can also be used for spectral radiance responsivity calibrations. Last but not the least, each layer of the LED-ISLSs can be manufactured independently and then the multiple layers can be assembled by straightforward alignment and packaging. The process is well suitable for quick, large volume production.
6.2 Performance improvements
Many aspects of the LED-ISLSs can be improved for better performance. First, the radiances of the LED-ISLSs manufactured in this work are at the classic level. For optical imaging microscopes with high sensitivity, the radiance responsivity is desired to be calibrated at low light (or even single photon) level. The emission intensity from the exit port of the miniaturized integrating sphere may be turned down simply by using a neutral density filter but the uniformity of the radiant exitance may be compromised since the relative standard deviation of the spatial photon flux is large. Many different methods such as adopting a high-speed rotating diffuser in the light path between the diodes and the integrating sphere may be applied to increase the randomness of the light beam paths so the temporally integrated signal on the CCD sensor over an increased amount of period from the low-light level radiance can form a uniform image with a minimal non-uniformity uncertainty. Efforts are underway towards the design of a good standard low-light radiance source. Secondly, the spatial distribution of the radiance of the LED-ISLSs is not uniform enough for optical imaging microscopes using a large NA objective lens. The aperture at the exit port is designed to have a very thin edge so the light can emit directly from the bottom of the integrating sphere. The entrance ports of the illumination from the LEDs can be further optimized and consequently the layout of the LED-ISLS assembly may need to be revised as well. A bigger integrating sphere may help increase the radiance uniformity in a larger solid angle and the trade-off between the size of the LED-ISLSs and the convenience of implementation will be considered under specific circumstances. Thirdly, commercially available LEDs can cover 350 nm to 1700nm. A typical LED offers a relatively broadband emission (see Fig. 2). For narrow spectral linewidth radiance responsivity calibration, laser-diode (LD) based miniaturized integrating sphere source can be developed with narrow spectral emission. Continuously tunable monochromatic light introduced into the integrating sphere via optical fiber may be needed for more comprehensive calibration.
A series of LED-ISLSs were manufactured as standard radiance sources for the radiance responsivity calibration of optical imaging microscopes. Each of the LED-ISLSs was produced via a multilayer assembly scheme, consisting of an LED source, a miniaturized integrating sphere, and an exit port. Four LED-ISLSs with different emission colors were manufactured, each of which had four radiance levels. The spectral characteristics, temporal stability, non-uniformity of the radiant exitance, and non-uniformity of the radiance of the LED-ISLSs were evaluated. The radiance of the LED-ISLS at different emission colors and radiance levels was calibrated using a two-aperture setup with a certified standard Si photodetector whose spectral responsivity is traceable to primary standards. The radiance of the LED-ISLSs is in the range of 5 W m−2 sr−1 to 69 W m−2 sr−1 and the combined standard uncertainty is 1.3%. The LED-ISLSs were applied to calibrate the radiance responsivity of a home-built optical imaging microscope with a standard relative uncertainty of 2.6∼2.9%. The advantages and possible performance improvement of the LED-ISLSs were discussed. This work offers a practical way for the radiance calibration of optical imaging microscopes.
National Key Research and Development Program of China (2017YFF0206103).
The authors thank Weimin Wang, Yinuo Xu, Yike Xiao, Dr. Xufeng Jing and Dr. Changyu Shen for useful discussions.
The authors declare no conflicts of interest.
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