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Abstract
Precise photon flux measurement of single photon sources (SPSs) is essential to the successful application of SPSs. In this work, a novel method, to our knowledge, was proposed for direct measurement of the absolute photon flux of single photon sources with a femtosecond laser multiphoton microscope. A secondary 2-mm-diameter aperture was installed under the microscope objective to define the numerical aperture (NA) of the microscope. The defined NA was precisely measured to be 0.447. An LED-based miniaturized integrating sphere light source (LED-ISLS) was used as a standard radiance source to calibrate the photon flux responsivity of the multiphoton microscope, with the defined NA. The combined standard uncertainty of the measured photon flux responsivity was 1.97%. Absolute photon flux from a quantum-dot based emitter was measured by the multiphoton microscope. The uncertainty of the photon flux was evaluated to be 2.1%. This work offers a new, to our knowledge, radiometric method for fast calibration of photon flux responsivity of microscopes, and absolute photon flux calibration of single photon sources.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Single photon sources (SPSs), with the unique photophysical properties, have great potential in quantum-related and optical metrological applications [1–4]. SPSs can emit identical photons at periodic intervals while being triggered by optical or electrical excitations [5,6]. The identical photons with a signature of indistinguishability, play an important role in applications of quantum information processing (QIP), including quantum cryptography [7,8], quantum simulation [9,10] and quantum computing [4,11]. The deterministic emission with one photon per excitation upon ideal situation, paves a new way to define the quantum candela – the SI base unit of luminous intensity [12], and provides a standard radiometric source for optical metrology applications at low optical power levels [13–15]. Numerous deterministic SPSs have been investigated, such as color centers in diamonds [16–20], quantum dots (QDs) [21–26], two-dimensional materials [27–30], carbon nanotubes (CNTs) [31–33], and single atoms/molecules [34,35], covering a wavelength range from deep UV [36] to telecom-band [37–39].
Extensive research efforts on the precise characterization of SPSs have been made for successful applications of SPSs, including the photon flux [15,40–42], the second correlation function (g(2)(0)) [43], and the indistinguishability [44]. To excite a single photon emitter, collect the fluorescence emission and measure the photon flux, confocal microscopes are widely applied. In this case, the excitation of the emitter is performed using a CW or pulsed laser source. The excitation laser should have higher photon energy than that from the emitted SPSs photons, the laser pulse width should be significantly smaller than the fluorescence lifetime of SPSs, and the pulse interval should be larger than the detector’s dead time. With this approach, the SPSs and the optics before the detector, including the fluorescence collection optics and the spectral filtering optics, can be seen as a combined object, and the measured photon flux includes the influence of the optics before the detector. By substituting the calibrated photon detector with a DUT detector, the quantum efficiency of the DUT detector can be calibrated. Several national metrological institutes (NMIs) have demonstrated the feasibility of using this approach to calibrate the detection efficiency of single photon avalanche detectors (SPAD) based on triggered SPSs such as color centers in diamonds [14,40], dibenzoterrylene molecules in anthracene nanocrystals [34], and InGaAs quantum dots [15,42].
Another approach of calibrating the photon flux of SPSs is to directly measure the photon flux of the source, excluding the influence of optics before the detector. This approach requires the calibration of photon flux responsivity of the microscope detection system with the knowledge of the numerical aperture (NA) of the microscope. Previously, we developed an LED-based miniaturized integrating sphere light source (LED-ISLS) to calibrate the radiance responsivity of optical microscopes [45]. Given a known NA of the microscope, the LED-ISLS can also be applied to calibrate the photon flux responsivity. However, precise assessment of microscope NA is no easy job, requiring meticulous optical interference measurement [46], light ray divergence angle measurement [47] or fluorescing angular distribution measurement [48]. Therefore, we proposed a new method of placing a secondary circular aperture under the microscope to define NA of the microscope and restrict light flux entering the microscope.
In this paper, we applied a secondary 2-mm-diameter circular aperture under a fs-laser-stimulated multiphoton microscope to define the microscope NA. Radiance calibrated LED-ISLS was also applied to calibrate the photon flux responsivity of the multiphoton microscope with the defined NA. A quantum-dot based emitter was used as a test sample and the absolute photon flux of the quantum-dot based emitter was calibrated.
2. Methodology
2.1 Realization of absolute photon flux calibration
A single photon source characterization setup was established based on a femtosecond laser stimulated multiphoton microscope (Fig. 1). A Ti:Sapphire ultrafast oscillator (Spectra-Physics, Tsunami Series) was pumped by a 532 nm CW laser with a maximum power of 10 W, emitting wavelength-tunable ultrafast laser pulse with typical pulse width smaller than 100 fs at FWHM. The repetition rate of the femtosecond laser pulse was 40 MHz. The femtosecond laser pulses passed through a series of optical components and were subsequently focused by a 16× microscope objective with a nominal NA of 0.8. Detectors were a CCD (Thorlabs, CS2100M-USB), and a photomultiplier (PMT) based photon counter (Hamamatsu, H10682-10), both located at back-focal-image plane. A fold mirror was used to switch the detecting path between two detectors.
Fig. 1. Using an LED-based miniaturized integrating sphere light source (LED-ISLS) and a secondary 2-mm-diameter aperture to calibrate absolute photon flux responsivity of a multiphoton microscope within a restricted NA. The microscope was subsequently used to calibrate the photon flux of a quantum-dot based emitter.
A secondary 2-mm-diameter circular aperture was used to define the microscope NA and restrict photon flux entering the microscope. The aperture was mounted on a 5-axis moving stage with 3-axis nm-precision translation and 2-axis rotation. To calibrate the photon flux responsivity of the multiphoton microscope, an LED based miniaturized integrating sphere light source (LED-ISLS) was placed under the microscope with a 100-µm-diameter pinhole from Cr-plating mask as the exit aperture. The radiance of the LED-ISLS was carefully calibrated. It is worth noting that the sample holder was also coupled to a 6-axis robot arm for potential angular emission investigation of the emitter.
To demonstrate the feasibility of using this multiphoton microscope for photon flux calibration of single photon sources, a CdSe/ZnS quantum-dot based emitter was used as a test sample to calibrate its photon flux within the defined NA.
2.2 Metrological traceability
The photon flux responsivity of the microscope, ηSYS,NA, can be expressed as follows:
Figure 2 summarizes the metrological traceability framework of using LED-ISLS and secondary 2-mm-diameter aperture to calibrate ФLED-ISLS,NA. Main parameters to be calibrated are listed as follows: the radiance at the secondary 2-mm-diameter aperture L, the exit aperture area of LED-ISLS (the pinhole area) As, the secondary 2-mm-diameter aperture area Aa, and the distance between the two apertures, d. The distance d was determined by a nanopositioning piezo linear translation stage. The travel distance of the stage was traceable to the length standards at NIM, China. Because of the spatial nonuniformity of LED-ISLS radiance, normal radiance LN and angular radiance distribution L(θ) were measured. The actual radiance at secondary 2-mm-diameter aperture L results from a combination of normal radiance LN and a correction factor f(NA) depending on the calibrated NA and the angular radiance distribution L(θ).
Fig. 2. Schematic overview of metrological traceability for the calculation of photon flux entering the detection system restricted by the secondary 2-mm-diameter aperture. Measurement for aperture areas, source radiance and inter-aperture distance were carried out in work package (WP) 1-3, respectively.
Before calibration, we estimated the photon flux of LED-ISLS entering the secondary 2-mm-diameter aperture. The radiance of LED-ISLS was tuned to the lowest level with radiance about a few tens of Wm-2sr-1. The photon flux of LED-ISLS was estimated to be a few nW, or of the magnitude 109 photons per second, given the wavelength range of LED-ISLS being 500-550 nm. Considering the typical photon flux of quantum-dot based emitters of the magnitude 106 photons per second, a neutral density filter with nominal optical density of 3.0 was placed in front of the PMT sensitive area while calibrating the photon flux responsivity using the LED-ISLS. The nominal quantum efficiency of PMT was about 10%, making the photon counts recorded by the PMT-based photon counter were a few hundred kHz. The OD3.0 filter also reduced the relative deviation of actual quantum efficiency of PMT to about 0.2%, due to the existence of PMT dead time while receiving multiple photons at the same time. The actual optical density, or attenuation coefficient of the filter ηF was calibrated using a standard collimated laser diode source and a PMT-based photon counter (Hamamatsu, H10680-10).
The neutral density filter was removed while calibrating the photon flux of the quantum-dot based emitter The photon flux of the quantum-dot based emitter NSPS, NA is expressed as:
3. Absolute calibration of multiphoton microscope photon flux responsivity
3.1 Calibration of pinhole area ASand secondary 2-mm-diameter aperture area Aa
The areas of 100-µm-diameter pinhole and secondary 2-mm-diameter aperture were calibrated by a flux comparison method in a uniform irradiance field. The irradiance field was generated from a 100-mm-diameter integrating sphere, illuminated by an LED source with a central wavelength of 532 nm (Fig. 3). A standard 4-mm-diameter aperture was used as reference aperture, which was precisely calibrated by standard area calibration apparatus using direct scanning method at Division of Dimensional Metrology at NIM, China. However, using the direct scanning method to calibrate the 100-µm-diameter pinhole and 2-mm-diameter aperture would bring large uncertainty. Therefore, we chose the photon flux comparison method to calibrate the areas of the two apertures for lower measurement uncertainty. Photon flux restricted by DUTs or the standard reference aperture was recorded by a standard photodiode (Hamamatsu, S1337). By comparing the photon flux restricted by the DUTs and that of the standard reference aperture, pinhole area AS is written as:
Fig. 3. Aperture area measurement setup. The spatial uniformity of irradiance field was evaluated by scanning with 1-mm-diameter aperture.
The pinhole glass substrate transmittance τ was measured by inserting the 100-µm-diamter glass pinhole between a 50-µm-diameter glass pinhole and the standard reference photodiode, and comparing the photocurrent before and after the insertion of the 100-µm-diameter pinhole. The transmittance τ was measured to be 90.0%.
The temporal instability of the integrating sphere source was measured with a monitor photodiode located inside the integrating sphere. Over a period of 140 minutes, the temporal instability was measured to be 0.016%. A 1-mm-diameter aperture was used to scan the spatial uniformity of the irradiance field from the integrating sphere source. Within the 4-mm-diameter aperture area, the spatial nonuniformity was estimated to be 0.1%.
The measured area of the 100-µm-diameter pinhole was 7.92×10−9 m2, and the measured area of the secondary 2-mm-diameter aperture was to be 3.02×10−6 m2.
3.2 Calibration of LED-ISLS radiance L
A two-aperture solid angle restricted method was used to calibrate the normal radiance LN of the LED-ISLS. The calibration setup can be refereed in Ref. [45]. A standard 9-mm-diameter precision aperture was used to define the solid angle observed by the standard photodiode (Hamamatsu, S1337). The distance between the 9-mm-diameter and the 100-µm-diameter pinhole was measured to be 64.0 mm by a stepper motorized translation stage (Thorlabs, LTS300). The photocurrent measured by S1337 photodiode was 22.83 pA (background signal subtracted). The normal radiance LN was measured to be 0.663 W m-2 sr-1.
We firstly simulated the diffraction effect of light rays from the 100-µm-diameter pinhole at the microscope objective with FRESNEL software (Fig. 4(a)). To simplify the modelling, we assumed the radiance from the 100-µm-diameter was spatially uniform after the homogenization effect from the miniaturized integrating sphere. The dash line cone in Fig. 4(a) represented the collection solid angle of a NA = 0.8 microscope objective. Due to the divergent light rays, diffraction effect only occurred at the edge of the detecting surface, and that can be neglected within the collection solid angle of NA = 0.8 microscope objective.
Fig. 4. (a) Diffraction effect from 100-µm-diameter pinhole of LED-ISLS simulated by FRESNEL software, and (b) radiance correction factor f(NA) with respect to the measuring NA of the microscope while using LED-ISLS to calibrate photon flux responsivity of microscope. The inset was the measured relative radiance distribution at different angular position from 0 to 47°.
The actual LED-ISLS had non-perfect radiance spatial uniformity due to the effect of the substrate glass, the Cr plating and the non-perfect diffuse reflection of the integrating sphere. Therefore, the spatial radiance distribution must be measured to correctly calculate the flux entering the detecting system. The spatial radiance distribution of the LED-ISLS was measured with a 1-mm-diameter aperture coupled to a PMT-based photon counter (Hamamatsu, H10680-10). The setup can also be referred in Ref. [45]., with an upgrade by mounting the PMT onto an angular rotation stage. At each measured angular position, the emission flux entered the aperture perpendicularly by adjusting the angular position of the PMT. After cosine-correction, the relative radiance distribution of the LED-ISLS at different angular positions was calculated. When the LED-ISLS was placed under the microscope, the actual radiance entering the microscope was the product of the normal radiance LN and the correction factor f(NA). The correction factor f(NA), was also calculated from the relative radiance distribution data (Fig. 4(b)). This correction factor f(NA) will be used to calibrate the photon flux entering the secondary 2-mm-diameter aperture in section 3.4.
3.3 Measurement of the distance between two apertures, d
The distance between the two apertures (100-µm-diameter pinhole of LED-ISLS and secondary 2-mm-diameter aperture) was determined by a nanopositioning piezo linear translation stage. As the 100-µm-diameter pinhole was placed at the focal point of the microscope while calibrating the photon flux responsivity, it is essential to evaluate the out-of-focus error of the microscope, which is an important uncertainty component for the final calibration result. The 100-µm-diameter pinhole of LED-ISLS closely clung to the lower surface of the secondary 2-mm-diameter aperture, with the pinhole located roughly in the middle of the secondary 2-mm-diameter aperture. The pinhole was placed near the focal point of the microscope objective lens, adjusted to horizontal position and a stream of 100-µm-diameter pinhole images at various relative z-positions near the focal point were taken by the microscope CCD (Fig. 5(a)). By naked-eye observation, the edge of the pinhole started to blur at certain distance from the focal point. We used a relative intensity contour radius evaluation method to determine the focal position and the out-of-focus error. The relative intensity distribution of the pinhole image at each z-position was mapped, and contour of specific relative intensity was taken out from the intensity distribution map. We used I = 0.4 (relative intensity) for analysis. By fitting the contour with non-linear least square fitting method, the radius of the contour R0.4 was calculated (Fig. 5(b)) in the units of pixel number. The contour radius versus relative z-positions was plotted after 7 independent measurements (Fig. 5(c)). The contour radius R0.4 was smallest in the focal area of the microscope objective with certain focal error. We used two relative z-positions, z1=-15µm and z2 = 20µm, to evaluate the focal point and out-of-focus error, as indicated in Fig. 5(c). The midpoint between z1=-15µm and z2 = 20µm was considered the focal point. The error bars indicated that z1=-15 position had a relative position error δ1 = 4.5µm and z2=-20 position had a relative position error δ2 = 8µm. Therefore, the out-of-focus error δ=(δ1+δ2)/2 = 6.25µm.
Fig. 5. Determination of focal position and out-of-focus error of the microscope. (a) A stream of 100-µm-diameter pinhole images around the focal position, (b) the relative intensity distribution of the pinhole image, and contour of relative intensity I = 0.4. The radius R0.4 was fitted by non-linear least square fitting algorithm, and (c) the contour radius of relative z-positions to determine the out-of-focus error to be ±6.25µm.
After the evaluation of the out-of-focus error, the pinhole of the LED-ISLS was detached from the secondary 2-mm-diameter aperture and left at the focal point of the microscope. The secondary 2-mm-diameter aperture was moved to the center position of the microscope optical axis, and then was moved upwards in z-direction from the focal point by 2 mm, making the two-apertures distance d = 2.000 ± 0.006 mm. The NA defined by the secondary 2-mm-diameter aperture was calculated to be 0.447. According to Fig. 4(b), the correction factor for radiance calculation, f(NA), was estimated to be 0.884.
3.4 Calibration of photon flux responsivity
With the results from Section 3.1-3.3, the photon flux entering the secondary 2-mm-diameter aperture ФLED-ISLS, NA can be calculated based on Eq. (2). ФLED-ISLS, NA was calculated to be 3.62 nW (or NLED-ISLS, NA(@520 nm) = 9.4×109 s-1 in photon flux).
The pinhole image taken from the microscope CCD is shown in the upper part of Fig. 6. The diameter of the pinhole image was evaluated to be 1.6 mm. Switching the photon collection path to PMT, the emission from the pinhole was fully detected by the 8-mm-diameter photon-sensitive area of the PMT. The neutral density filter was installed in front of the PMT to attenuate the measured photon flux. The recorded photon flux rate of PMT was 177.804 kHz (background subtracted). At this photon flux rate, the relative deviation of PMT quantum efficiency due to the simultaneous multi-photon strikes on PMT was kept as low as 0.2%.
Fig. 6. pinhole image of LED-ISLS on microscope CCD with an estimated diameter of 1.6 mm and the relative non-uniformity of PMT quantum efficiency scanned by a laser diode source. The relative non-uniformity within the pinhole image area was about 0.6%.
The photon flux responsivity of the microscope (with neutral density filter), ηSYS, NA, at the wavelength range of LED-ISLS was calculated to be 49.1 s-1pW-1.
The attenuation coefficient of the neutral density filter ηF was measured to be 6.65×10−4 at photon flux rate of the magnitude a few hundred kHz.
The relative non-uniformity of PMT quantum efficiency across the 8-mm-diameter photosensitive area of the PMT was scanned by a thermostatically-controlled collimated laser diode source (λ=520 nm, temporal instability∼0.01%) and a 10× objective lens. The focal spot size of the laser diode source was a few tens of µm. The scanned PMT quantum efficiency non-uniformity result is presented in Fig. 6. Within the 1.6-mm-diameter pinhole image area, the relative non-uniformity was about 0.6%, which would be considered in the uncertainty analysis.
The key parameters for multiphoton microscope photon flux responsivity calibration results are summarized in Table 1.
Table 1. Summary of key parameters for photon flux responsivity calibration
The uncertainty of the photon flux responsivity is analyzed and summarized in Table 2. Based on equation (1-2), uncertainties of all parameters involved in calculation of ηSYS,NA contribute to the final uncertainty of ηSYS,NA. The uncertainty of normal radiance of LED-ISLS was 1.3%, in accordance with Ref. [45]. The uncertainties of 100-µm-diameter pinhole area and secondary 2-mm-diameter aperture area were measured to be 0.4% and 0.2%, respectively. The uncertainty of two-aperture distance d was calculated to be 0.3% according to the out-of-focus error in Section 3.3, thus its contribution to photon flux responsivity uncertainty should be doubled to be 0.6%. The uncertainty of radiance correction factor f(NA) is contributed from the uncertainty of measured NA and the interpolation uncertainty in Fig. 4(b). The uncertainty of measured NA was calculated to be 0.85% and the uncertainty of interpolation was estimated to be 0.5%. Therefore, the uncertainty component from radiance correction factor f(NA) was evaluated to be 1.0%. The uncertainty component of PMT quantum efficiency non-uniformity was measured to be 0.6%, the uncertainty component from multi-photon strikes simultaneously on PMT was evaluated to be 0.2%, and the uncertainty from measurement repeatability was 0.5%. The combined standard uncertainty of photon flux responsivity was evaluated to be 1.97% (k = 1).
Table 2. Uncertainty analysis for photon flux responsivity of multiphoton microscope
4. Demonstration of absolute photon flux calibration of a quantum-dot based emitter
A quantum-dot based emitter was tested to demonstrate the feasibility of using the NA-defined, photon flux responsivity calibrated multiphoton microscope to measure the absolute photon flux. CdSe/ZnS quantum dot solution (5 mg/mL, solved in methylbenzene, peak emission wavelength 530 nm, FWHM 20 nm) was diluted by 104 times and spin-coated uniformly onto a glass slide. The sample was placed under the multiphoton microscope with the 2-mm-diameter aperture and stimulated by 40 MHz femtosecond laser pulse at excitation wavelength of 830 nm. Using galvo-scanner of the multiphoton microscope to scan across the sample, a quantum-dot cluster with clear fluorescence emission was located under the objective lens and the fluorescence image was taken by the microscope CCD with exposure time of 2500 ms (inset of Fig. 7). After switching the detection path to PMT-based photon counter, photon flux rates at different laser powers were measured (Fig. 7). The photon flux increased almost linearly between laser power 0.3 to 0.9W, before reaching saturation after 0.9W. The photon flux recorded by PMT can be translated to the absolute photon flux of the quantum-dot based emitter at each laser power, according to Eq. (3). For instance, at laser power of 0.516W, the photon flux recorded by PMT was measured to be 135.03 kHz (background subtracted). According to Eq. (3), the absolute photon flux of the quantum-dot based emitter was 4.78×106 s-1. It is noteworthy to point out that the quantum-dot based emitter stimulated by femtosecond laser pulse might be a cluster of quantum dots, and the photon flux calculated here does not represent the photon flux from a single quantum dot stimulated by 40 MHz fs laser pulse.
Fig. 7. Dependence of quantum dot emission photon counts on laser power. Inset of top left corner: comparison of relative spectral intensity of LED-ISLS and quantum dot emission, and inset of bottom right corner: Emission from quantum-dot based emitter stimulated by 40 MHz fs laser pulse, recorded by multiphoton microscope CCD with exposure time of 2500 ms.
We also compared the relative spectra of our calibration source LED-ISLS and the fluorescence from the quantum-dot based emitter. The center spectral position of LED-ISLS was 520 nm and that of quantum dot fluorescence was 530 nm (inset of Fig. 7). The spectral difference will inevitably bring uncertainty while using the photon flux responsivity data calibrated by the LED-ISLS to measure the absolute photon flux of quantum-dot based emitter. New calibration sources with narrow-band LED or LD emission based on miniaturized integrating sphere are under investigation currently. Nevertheless, it is already proved in this work that with our current LED-ISLS, together with the 2-mm-diameter aperture, it is feasible for absolute photon flux calibration of quantum-dot based emitter.
The uncertainty components of quantum-dot based emitter photon flux calibration consist of the uncertainty of photon flux responsivity of the multiphoton microscope (1.97%), the unmatched spectra of LED-ISLS and quantum dot fluorescence (0.2%), the short-term fluorescence stability (0.5%), and the measurement repeatability (0.5%). The overall uncertainty of quantum dot photon flux calibration was evaluated to be 2.1%.
5. Capability of calibrating photon flux of single photon sources
In section 4, we demonstrated the capability of the photon flux responsivity calibrated multiphoton microscope to measure the photon flux of quantum-dot based emitter. We haven’t confirmed the single photon emission characteristic of quantum-dot based emitter via HBT experiment due to the possible clustering of multiple quantum dots. However, the calibrated photon flux of the quantum-dot based emitter was of the magnitude 105 to 106 photons per second, in the same magnitude of photon flux emitted from real single photon sources, such as monodispersed CdSe/ZnS quantum dots, NV centers etc. Provided a well-dispersed quantum dots sample was tested and an individual quantum dot was located under the multiphoton microscope, the setup is capable of measuring the photon flux of the quantum dot SPS. In our following work, we will focus on the realization of measuring photon flux of real SPSs by this setup.
6. Conclusion
In this paper, a novel method was proposed to directly measure the absolute photon flux of SPS with a multiphoton microscope. A secondary 2-mm-diameter restrictive circular aperture was precisely located under a multiphoton microscope to define the NA of the microscope. The defined NA was measured to be 0.447. A LED-based miniaturized integrating sphere light source (LED-ISLS) was used as a standard radiance source to calibrate the photon flux responsivity of the multiphoton microscope with aperture-defined NA. The combined standard uncertainty of calibrated photon flux responsivity was 1.97%. The multiphoton microscope was subsequently applied to stimulate a quantum-dot based emitter and the absolute photon flux of the emitter was calibrated. The overall uncertainty of photon flux from the quantum-dot based emitter was evaluated to be 2.1%. This work offers a new radiometric method for fast calibration of photon flux responsivity of microscopes, and absolute photon flux calibration of single photon sources.
Funding
National Key Research and Development Program of China (2017YFF0206103).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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