High-Repetition Rate Broadband PumpâProbe Microscopy | The

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High-Repetition Rate Broadband Pump−Probe Microscopy Geoffrey Piland† and Erik M. Grumstrup*,†,‡ Department of Chemistry and Biochemistry, and ‡Materials Science Program, Montana State University, Bozeman, Montana 59717, United States

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ABSTRACT: Pump−probe microscopy has recently emerged as an important tool for characterizing the effects of nanoscale chemical and compositional heterogeneity on the optoelectronic properties of material systems. This article describes the development of broadband pump−probe microscopy, which utilizes a high-speed line camera and high repetition rate amplified fiber laser to collect full transient spectra at 30+ kHz and with sub 100 fs temporal resolution. The broadband imaging and spectroscopic capabilities of the technique are demonstrated on individual micron-sized lead halide perovskite domains. Also discussed are several challenges associated with collecting broadband transient spectra from sub-micron sample areas, including the importance of careful design of imaging optics to minimize the effects of spherical and chromatic aberrations, detector considerations, and the importance of spot size effects on absolute signal size.

1. INTRODUCTION

schemes, quantitative interpretation of spectra, and approaches for overcoming chirp in highly dispersive optics.

The combination of high spatial and temporal resolution enabled by pump−probe microscopy (PPM) provides the ability to correlate specific ultrafast spectroscopic observables to sub-micron structural and compositional information. As a result, PPM has delivered important new insights into the effects of grain boundaries, edge states, surface interactions, and chemical gradients on the spatial and energetic dynamics of excited states in semiconducting and metallic systems. Numerous examples of the power of this technique exist, wellsummarized by some recent review articles with applications in materials and biological systems and as an analytical tool.1−3 Most of the works to date utilizing PPM have employed single wavelength measurements, in which transient kinetics or images are collected on a single element detector, often using a lock-in amplifier to demodulate the change in transmitted (or reflected) probe light. Here, we describe the development of broadband PPM, which leverages the recent emergence of high repetition rate, ultrafast fiber lasers, paired with high-speed CMOS line cameras as detectors. The instrument provides the ability to collect transient spectra with >100 nm bandwidth from a sub-micron-scale sample volume, while maintaining signal-to-noise levels that rival lock-in detection. While promising, several important instrumentation challenges, which are unique to broadband transient microscopy, must be overcome. This article discusses these challenges and provides a guide to researchers interested in developing a broadband pump−probe microscope. We first compare single wavelength and broadband PPM with common ensemble-type transient absorption (TA) instruments. We then discuss the instrument in detail and demonstrate the utility of the technique by characterizing individual lead halide perovskite domains. Finally, we examine the significant technical challenges associated with broadband PPM, including imaging aberrations, both at the sample and at the detector, modulation © XXXX American Chemical Society

2. RESULTS AND DISCUSSION 2.1. Microscopic Versus Ensemble Spectroscopies. At a superficial level, the approach for conversion from an ensemble TA apparatus to a microscopic setup is as simple as inserting a microscope objective into the beam path, providing a means to image and position the sample and proceeding to collect transient data as usual. There are, however, several more subtle considerations that make microscopy more challenging than conventional TA spectroscopy. The most salient difference is that the sample interaction volume is much smaller than in ensemble techniques. Assuming a reasonably well-designed optical apparatus, probe volumes for a visible microscope are on the order of 1 μm3, approximately 106 to 107 smaller than what might be interrogated in a conventional TA instrument. While the reduced probe volume is clearly by design, there are a number of important consequences for transient spectroscopies. The first is that pulse fluences must be much lower, both because the absolute number of chromophores is much lower, and more practically, in order to mitigate sample heating and prevent damage. It is not uncommon, for example, that pulse energies on the order of 10−100 fJ are employed in a PPM. The challenges associated with low pulse energies are often combatted with high repetition rate lasers, so that significantly more signal averaging can be performed during the time of an experiment and also to enable rapid imaging. Thus, typical signal sizes are much lower in PPM than in ensemble techniques, with ΔI/I ≈ 10−4 typical and ΔI/I ≈ 10−6 not uncommon. Such high repetition rate, low signal measurements have until recently been performed Received: April 24, 2019 Revised: June 18, 2019 Published: June 28, 2019 A

DOI: 10.1021/acs.jpca.9b03858 J. Phys. Chem. A XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry A

Figure 1. Diagram of the broadband pump−probe microscope. AOM: acousto-optic modulator, BS: beam splitter, GV: galvanometer mirrors, SCG: supercontinuum generation, SF: spatial filter, SHG: second harmonic generation.

To compensate for the dispersive optics (including the high NA objective) in the beam path, the probe is sent through a single prism pulse compressor followed by a single grating pulse compressor.9,10 Utilizing a prism compressor and a grating compressor in series allows for compensation of both the second and third order dispersion, while the single element design of these compressors minimizes the spatial chirp of the beam by reducing the chance for alignment errors. Careful alignment of the prism and grating compressors (as well as all other optics in the beam-line) is critical to ensure optimal dispersion compensation and to minimize spatial aberrations in the beam at the sample plane. Because the laser spot sizes are focused to near diffraction-limited spots, the spatial resolution in imaging, the effective temporal resolution, and the pump− probe spectral overlap throughout the bandwidth of the probe are highly sensitive to optical system alignment. The pump line is passed through an acousto-optic modulator (AOM, AA Opto Electronic) to modulate the 1 MHz pulse train at 31.25 kHz (16 pulses on, 16 pulses off). The chopped beam is focused onto a 1 mm type 1 BBO for second harmonic generation (SHG, 517.5 nm) and then sent through a 1:1 telescope with a 20 μm pinhole at the focus. The telescope and pinhole combination serves as both a spatial filter to remove undesired spatial modes and to independently control the focal plane of the pump relative to that of the probe at the sample. The pump beam is coupled onto a motorized delay stage to provide the pump−probe delay time (Δt) and then directed onto a two-mirror galvanometer system coupled to a 4-f lens system to arbitrarily position the pump beam in the focal plane (xy plane). Pump and probe beams are combined with a broadband 70:30 beamsplitter before entering the 0.90 NA 100× microscope objective (Olympus MPlanFL-N). A refractive objective was used over a reflective objective as we found that both the transmission efficiency and the imaging quality with the refractive objective was much higher. At the sample plane, cross correlation of the uncompressed SHG pump and compressed probe on a SiC photodiode gave an instrument response of 400 fs, limited by the pump duration. Cross correlation of the probe with the compressed output of a homebuilt OPA11 yielded an instrument response of 100 fs, illustrating the possibility for further improvement of the temporal response of the instrument, without changing to reflective optics. The sample is mounted onto a piezoelectric stage with 0.2 nm positioning precision (Mad City Labs, Nano-H100) as well as a larger manual x−y translation stage to allow both coarse and fine positioning of the beams on the sample. The probe light can be collected in reflection (epi) or transmission

exclusively using lock-in amplifiers, which have the necessary frequency bandwidth and dynamic range to obtain useful S/N ratios under such conditions. A second challenge of PPM comes from the interaction volume. Aside from the well-known considerations like spherical and chromatic aberrations which limit imaging performance and are intrinsic to using high NA objectives, the spectroscopic component of PPM is nontrivial. Because the transient signal is dependent on the field intensities of both pump and probe, and because the two pulses are typically focused to near diffraction-limited (Gaussian-like) spots, the excited state population density is anisotropic in the excitation volume. There are important consequences of this excitation anisotropy. First, because the excitation density is significantly higher in the middle of the pump spot than at the edges, the experimentalist must be careful that the sample is photoexcited in the linear regime throughout the pump pulse area or risk observing highly nonlinear behavior in the middle, conflated with linear behavior at the edges.4,5 Second, signal intensities depend on the relative spatial overlap of pump and probe. Thus, even under diffraction-limited conditions, quantitative comparisons between different probe spectral regions require that the transient signal magnitude be renormalized by the product of pump and probe spatial profiles. We discuss this issue further in Section 2.4.2 below. Finally, Chung et al. have shown that focal depth variation can induce phase shifts in the nonlinear optical response, in principle causing complete sign reversal of the transient response depending on the detection geometry.6 This concerning effect is especially relevant for measurements performed in transmissive mode when a low NA objective is used for collection. Further investigation of this effect is needed, particularly for samples that are continuous throughout the depth of focus; however, it illustrates the need for careful experimental design. Thus, while PPM microscopy can provide exceptional insight into sample heterogeneities and defects, there are added challenges associated with the increased spatial resolution. As outlined below, these challenges are compounded with a broadband probe. 2.2. Instrument. Our homebuilt broadband PPM (Figure 1) is pumped by a 40 W, 1 MHz 1035 nm diode-pumped femtosecond laser (Coherent Monaco) with a minimum pulse duration of 290 fs. Of the available 40 μJ, a fraction is used for pump (3 μJ) and probe (1 μJ) lines. The probe is focused onto a 1 cm thick YAG crystal with a 100 mm focal length lens to produce a white light continuum (WLC).7,8 The WLC is collimated with a 50 mm aspheric, achromatic lens, and the IR component is subsequently rejected using a bandpass mirror. B


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These regions are often near edges or exhibit significant surface roughness, which suggests that scattering, which reduces the overall FP mode contrast,13 is likely responsible for the deviation. It is important to note, however, that additional excitation effects such as band-gap renormalization, band filling, stimulated emission, and free carrier absorption can all contribute to the overall optical response observed in the reflective and transmissive spectra, particularly as the probe energy approaches the band-edge resonance. The ability to measure broadband transient images can, in principle, provide a number of important correlations between the morphology of the sample and the photophysical response. In principle, careful analysis of both equilibrium and transient images can provide structural information like domain thickness (akin to spectroscopic ellipsometry) as well as pump-induced changes to the real and imaginary parts of the dielectric function. For example, Harel and co-workers have utilized broadband PPM (at 2.5 kHz) to reveal shifts in the transmission spectrum of lead halide perovskite domains, attributed to localized photoexcited population heterogeneity.14 2.3.2. Time-Resolved Transient Spectra: Nanoscale Spectroscopy. Collecting spatially overlapped broadband kinetics, in which the pump and probe pulses are spatially overlapped at the same position in the focal plane, is the closest analogy to measurements performed with a conventional pump−probe instrument. As in an ensemble measurement, Δt is varied using a computer-controlled delay stage. For PPM, however, the spot size of each pulse is on the order of 1 μm, making careful delay stage alignment particularly important, as a slight misalignment will quickly walk the two beams off of spatial overlap. Acquisition of transient kinetics at a single location takes approximately 1−2 min, depending on signal size and desired time resolution. In panels A and B of Figure 3, we show spatially overlapped ΔR/R images of the same MAPbBr3 perovskite domain shown in Figure 2, spectrally integrated between 570−580 and 620− 630 nm, respectively. The pump−probe delay is Δt = 1 ps for both images. By comparing the two images, it can be seen that the spectral response of the domain strongly varies from location to location. We have found that such comparisons are valuable tools for understanding the optical response of microscale domains, often providing insight into how specific spectral features arise from the local morphology. For example, panel C shows a comparison of ΔR/R spectra collected from the regions highlighted by the green and red circles in panel A. While the optical response is determined by the same photogenerated species, the two transient spectra differ significantly because of thickness differences in the domain. The region near the red circle is thicker and so the transient spectrum exhibits a stronger wavelength-dependent FP pattern. On the other hand, the optical response from a location where the domain is thinner (green circle) is relatively flat between 600 and 700 nm and is dominated by a broad, non-modulated decrease in transient reflection. We note that such spectra are automatically acquired at every pixel of the image, so no added experimental time is required to make spectral comparisons between different locations. Panel D shows the broadband time-resolved kinetics collected from the green circle location. Note the red edge of the band-edge emission band near 550 nm in panel C. Panel E shows three traces illustrating the kinetics at three different wavelengths (600, 625, and 675 nm). The prism and grating compressors were adjusted to ensure

(Nikon TU Plan Apo, 0.90 NA, 100×) modes. In either case, the probe is passed through a spatial filter and focused into a homebuilt transmissive spectrometer which disperses the continuum onto a 2048 pixel line camera (Teledyne DALSA OctoPlus) with 200 μm tall pixels (see further discussion in Section 2.4.1 below). Pump-on and pump-off spectra are collected with a maximum line rate of 125 kHz using a custom data acquisition script written in LabVIEW. 2.3. Spectroscopy and Imaging. Three operating modalities are possible with the microscope: spatially overlapped imaging, spatially overlapped kinetics, and spatially separated imaging. Each mode of operation provides a different type of data class, and in broadband probing, a different set of problems that must be overcome to ensure the data collected are robust and free from artifacts. Below, we outline each mode of operation before addressing the challenges of the optical design. 2.3.1. Spatially Overlapped Imaging: Structural Correlation. For spatially overlapped imaging, the pump and probe pulses are spatially overlapped in the focal plane at a fixed delay time, and the sample is raster-scanned using a piezoelectric translation stage. While dependent on signal to noise levels, a typical 100 × 100 pixel image can be collected in 3−4 min of experimental time. Figure 2 shows spatially overlapped imaging

Figure 2. Spatially overlapped imaging. (A) Scanning electron micrograph of a MAPbBr3 perovskite domain. Scale bar: 5 μm. (B) ΔR/R image of the domain shown in panel (A) collected at Δt = 1 ps. The image is obtained by spectrally integrating the optical response between 620 and 630 nm. (C) Corresponding ΔT/T image of the perovskite domain collected at a Δt = 1 ps. (D) Profile comparison collected from the dotted line in panels (B,C).

of a single MAPbBr3 (methylammonium lead tribromide) perovskite domain on a glass microscope slide. The images in panels B and C reflect the spectrally integrated signal from 620 to 630 nm. Comparison of the SEM (panel A) to the ΔT/T (panel C) and ΔR/R (panel B) images shows good correlation of the images to the structure. Generally, the ΔT/T and ΔR/R images show inversely correlated contrastthat is, increases in transient reflectivity typically correlate to decreases in transient transmission. These alternating fringes result from Fabry− Perot (FP) interference of the probe beam in the MAPbBr3 domain. Photoexcitation perturbs the dielectric function of the material, which in turn causes shifts in the (probe) FP mode spatial positions.12 Although the complementarity between ΔT/T and ΔR/R images is generally present across the entirety of the domain, there are regions that appear to deviate. C


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mode of operation, the pump is typically held fixed at a particular location on the sample and the probe is scanned over the field of view of the microscope to record the optical response of the sample at a fixed Δt. This operation is analogous to a spatial convolution; thus, the roles of the two beams may be reversed without changing the measurement, provided the sample is locally homogeneous. In our apparatus, the probe is held fixed at a particular location and the pump is spatially scanned so that probe alignment on the detector can be maintained without complicating the optical apparatus with descanning optics. The typical acquisition time for a spatially separated image at a set delay time is approximately 3−4 min, depending on the signal size of the material. In spatially separated imaging, the PPM signal intensity is given by (in one dimension) IΔx(t ) =

ij −4 ln(2)Δx 2 yz a0 zz expjjj zz β(t ) jk β(t )2 {

(1a)

β(t ) = (γ12 + γ2 2 + 16Dt ln(2))1/2

(1b)

where a0 is an arbitrary scaling factor, γ1 and γ2 are the pump and probe spatial full width at half maxima (fwhm), respectively, D is the ambipolar diffusion coefficient, and Δx is the spatial separation between the pump and probe beams. At early delay times, before the excited states have moved from their initial position, the observable is a Gaussian shaped spot like that shown in Figure 4A, with a fwhm determined by spatial convolution of pump and probe spots. At longer delays times, the photogenerated excited states may undergo transport, either through drift in the case of an applied field or via diffusion. In the limit of diffusive motion, the squared width of the distribution increases linearly with time (eq 1b and Figure 4B), with a slope directly proportional to the diffusion coefficient (Figure 4C). When collecting such images using a broadband probe, the opportunity arises to compare the diffusion constants of excited states with different resonance energies. While this capability is not relevant for equilibrated populations, it may be essential for understanding transport under non-equilibrium conditionsfor example, in cases of ballistic transport,5,18 or during energetically downhill excitonic/charge hopping.19 2.4. Instrument Considerations and Challenges. The detection of full transient spectra from micron-scale regions requires careful consideration of imaging optics, signal sizes, and noise levels. Below, we discuss several areas where unique

Figure 3. Time-resolved transient spectra. (A) ΔR/R image of the perovskite domain shown in Figure 2 integrated from 570 to 580 nm and (B) from 620 to 630 nm. Both images were collected at Δt = 1 ps. (C) Comparison between ΔR/R spectra (Δt = 1 ps) collected from locations indicated by green and red circles in panel (A). (D) Broadband kinetics measured at the location indicated by the green circle in panel (A). (E) Kinetics traces at 600, 625, and 675 nm with the colors matching the dashed lines in panel (D).

that the majority of the broadband probe bandwidth arrives at the sample within 100 fs, compensating for the dispersion introduced by the objective. While further improvements in temporal resolution are possible, nonconventional optics (Fourier domain pulse shapers) are likely necessary to remove the higher order dispersion that contributes to pulse broadening. 2.3.3. Spatially Separated Imaging: Excited-State Transport. The final operational mode of PPM is spatially separated imaging, which can provide a direct probe of exciton, plasmon, and free carrier transport in the sample (Figure 4).15−17 In this

Figure 4. Spatially separated PPM. (A) ΔR/R spatially separated image of the location indicated by the green circle on the MAPbBr3 domain shown in Figure 3A at λprobe = 620−630 nm. (B) Slices in the y-axis of spatially separated images at various time delays with overlaid Gaussian fits. (C) Change in fwhm2 of the spatially separated image vs Δt with a linear fit. D is calculated from the linear fit slope using eq 1b. D


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Figure 5. Comparison of the spectral image at the detector plane. (A) Image obtained using a f/4 CZ commercial spectrograph. (B) Slices from the image in panel (A) illustrating the difference in the spatial profile at two different wavelengths (solid: 640 nm, dashed: 760 nm). (C) Image obtained using a homebuilt transmissive spectrograph. (D) Slices from image (C) illustrating the difference in the spatial profile at two different wavelengths as marked in panel (C). (E) Diagram of collection and detection optics used after the sample plane.

spherical and chromatic aberrations, which are particularly challenging to overcome in high index materials like inorganic semiconductors. While the reduction in imaging performance can be mitigated by optimizing the tube lens position and focal length, sample-induced aberrations cannot be completely eliminated.20 Additional aberrations caused by the substrate are problematic for transmissive measurements but are minimized for reflective imaging. Panels B and D show profiles from the detector plane images of the CZ and homebuilt spectrographs, respectively. The solid and dashed profiles in each panel indicate the vertical profiles at 640 and 760 nm, as indicated by the solid and dashed lines in panels A and C. For the CZ data in panel B, comparison of the vertical profile at 640 nm (solid) to that at 760 nm (dashed) reveals the well-known “bowtie” astigmatism endemic to CZ spectrographs. At 760 nm (and on the blue edge), the image is out of focus, meaning that unless the detector pixels are larger than ∼400 μm, the full beam profile will not be integrated to form the spectrum. In the limit of a completely homogeneous beam profile, the consequence of not integrating over the full beam profile is simply fewer counts on the detector. However, close examination of Figure 5A shows that the beam profile is not homogeneous. Rather, there is distinct structure in the beam, which is a consequence of sample-induced spherical and chromatic aberrations. Integrating over such structure before calculating transient spectra is essential to acquiring data that are both qualitatively and quantitatively correct. We have found that if the detector pixel height does not encompass the entirety of the beam profile, both the amplitude and sign of transient spectral features can change depending on vertical alignment on the detector. To combat these artifacts and to maximize optical efficiency of the instrument, we designed and built a simple spectrograph based on two multi-element commercial camera lenses and a 600 g/mm volume phase holographic grating (VPHG, Wasatch Photonics).21 We used a VPHG rather than a standard transmissive grating for its high efficiency and to eliminate ghosting from higher diffraction orders. The excellent off-axis imaging, compensation for chromatic aberrations, and the high NA of the camera lenses provide far-improved imaging and collection efficiency at the detector plane in comparison to the CZ spectrograph. A further benefit, given

challenges exist for implementing high repetition rate, broadband PPM. 2.4.1. Imaging Aberrations and Spectrometer Design. Modern cameras capable of high frequency line rates employ pixels that are significantly smaller than the active area on many single element detectors. Generally, pixel sizes range from 10’s to 200 μm in height. Imaging the entire beam onto such an array requires that careful attention be paid to the light collection optics, sample-induced aberrations, and spectrograph imaging optics. In Figure 5, we compare the imaging characteristics of two types of spectrometersa traditional reflective Czerny− Turner (CZ) spectrograph and a homebuilt all refractive spectrograph using commercial camera lenses (Nikon AF-S Nikkor 50 mm f/1.8G). Panels A and B show data collected from a commercially available 300 mm CZ spectrograph with a f/4 aperture ratio. Panels C and D show data collected from our homebuilt spectrometer. In both cases, the WLC was focused onto a single crystal ∼1.5 μm thick formamidinium lead bromide perovskite domain (index of refraction, n = 2.45) deposited on a 1 mm thick borosilicate cover slip (n = 1.52). The transmitted light was collected with a Nikon 0.90 NA 100× apochromat objective (TU PLAN APO EPI), coupled through a spatial filter with 2 in. diameter 200 mm achromatic doublet lenses and directed toward either spectrometer via a flip mirror. The beam was focused onto the spectrographs’ image planes using 50 mm aspherical doublet lenses. The spectrally dispersed probe beam at the detector plane was imaged with a monochrome CMOS camera (FLIR BFS-U316S2M-CS). Given the tube lens focal length of the collection objective is 200 mm, the imaging system (in the no-aberration limit) results in a magnification ratio of 25× at the first image plane of the spectrograph. Therefore, assuming a spot size of ∼1.0 μm at the sample plane, and a 1:1 magnification ratio of the spectrograph, the spectrally dispersed beam should be imaged to a height of 25 μm at the detector position. When no sample is present in our microscope (no aberrations), we obtain a beam profile at the detector plane comparable to the predicted 25 μm (not shown). However, when a sample is present, the optimally focused beam profile is significantly larger at the detector plane of both spectrographs (panels A− D). This broadening is a consequence of sample-induced E


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point spread function, spatially separated images may be collected (at a delay time before carrier or exciton transport has significantly broadened the profile). The fwhm of the convolved pump−probe profile (measured as a function of wavelength) is then used as a multiplicative factor to renormalize the spectra. The comparison between the ideal correction function (given by eq 2) and that measured on our instrument is given in Figure 6A. Panel B shows the effects of renormalization on transient spectra. While the results are subtle in this case, they may become more pronounced, particularly if objectives with minimal corrections for chromatic aberration are used in an instrument. 2.4.3. Modulation Schemes and Signal to Noise. An essential component of high repetition rate PPM is a multielement detector capable of high spectral acquisition rates. Modern CMOS cameras are now capable of line rates greater than 100 kHz, which provides the ability to detect signal sizes that previously were only accessible with lock-in detection.22 The camera we utilize acquires lines at a maximum frequency of 125 kHz with 12-bit resolution. To collect a pump−probe signal, the simplest modulation scheme would apply a 50% duty cycle square wave at 62.5 kHz to the pump pulse train. Probe spectra could then be collected at 125 kHz, with the difference between subsequent spectra determining the change in probe transmittance (or reflectance). Unfortunately, the camera we utilize alternates between two analog-todigital converters (ADCs) for subsequent lines. Because of differences in the ADC fixed pattern noise (both PRNU photoresponse non-uniformity, and DSNUdark signal nonuniformity), calculation of transient spectra under this modulation scheme results in a specious background signal that varies from pixel to pixel and with total number of counts. The difference between sequential dark lines collected with the camera varies between 1 and 5 counts, depending on the pixel. Assuming the full dynamic range of the detector is accessible for a measurement, then the background signal magnitude is ΔI/I ≈ 10−3, an unacceptable level for most time-resolved spectroscopic applications. To overcome this noise source, we modulate the pump at 31.25 kHz while still acquiring spectra at 125 kHz, as illustrated in panel A of Figure 7. This scheme ensures that the fixed pattern noise arising from the two ADCs is equally represented in pump-on and pump-off spectral measurements. The drawback of this scheme is a modulation rate reduced by a factor of two from optimal. Nevertheless, because the vast majority of the noise in both pump and probe lines occurs at frequencies lower than 30 kHz, collecting spectra with signal sizes, ΔI/I ≈ 10−5 (panel C) is readily achievable. In panel D, we show a comparison of kinetics collected using a photodiode and lock-in amplifier to those collected using the line camera. In both cases, a 10 nm portion of the spectrum centered at 600 nm was integrated to produce the displayed kinetics. Settings were optimized for a dwell time of 1.5 s at each pump−probe delay time. The signal to noise levels are comparable in the two schemes. One final note regarding the use of high-speed line cameras for transient spectroscopies: The high-speed ADCs used in the cameras typically have a maximum bit depth of 12. Thus, the minimum relative change in intensity (ΔI/I) that can be measured for any single measurement is 1/212 or 2.4 × 10−4. Any change in intensity smaller than the difference between two sequential bits will be rounded to the nearest bitthis effect is the well-known quantization error intrinsic to ADCs.23

that the lenses are available off the shelf from many sources, is a moderate overall cost of the spectrograph. As is shown in panels C and D, the vertical beam profile is nearly identical across more than 200 nm of the spectrum, exhibiting negligible astigmatism. In addition, the beam profile falls entirely within the 200 μm pixel height of the line camera (pixel height is indicated by the thin grey lines in panels B and D), ensuring that all probe light from the sample is integrated in calculation of the spectra. 2.4.2. Renormalization of Transient Spectra. In conventional pump−probe spectroscopy, pump and probe optics are often optimized to ensure that the probe spot is much smaller than the pump spot at the sample. By doing so, the assumption can be made that the excitation density interrogated by the probe is homogeneous, regardless of wavelength. In PPM, this assumption is no longer valid because the pump and probe are ideally both at the diffraction limit. As a result, the absolute signal magnitude will be wavelength-dependent, even in the limit of uniform spectral response from the sample and in the limit of no chromatic aberrations. Assuming the spatial offset between the beams Δx = 0 and Δt = 0, eq 1a can be rewritten as I (λ ) =

a0 = β(λ)

a0 2

(γ1(λ) + γ2(λ)2 )

(2)

Equation 2 provides a theoretical normalization function that accounts for the wavelength dependence of the pump and probe spot sizes. In panel A of Figure 6, we show the calculated normalization curve (red) assuming the widths of pump and probe are diffraction-limited, γ(λ) = λ/2NA, with a pump wavelength of 517.5 nm. When chromatic aberrations are present in the imaging system, the curve will differ from the ideal case given by eq 2. In general, it is expected that the normalization function will vary from lab to lab depending on the objectives and other optics in the beam line. To measure the effective pump probe

Figure 6. Renormalization due to pump probe overlap effects. (A) Red trace shows the relative weighting factors calculated by a single point convolution of pump and probe, assuming Gaussian spatial beam profiles. The black curve shows the actual response of our instrument, measured using the transient response of a 100 Si wafer. The difference in the curves arises from chromatic aberrations induced by the imaging optics. (B) Transient spectra from the MAPbBr3 domain shown in previous figures, uncorrected and corrected for effective point spread function of the measurement. F


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Figure 7. Considerations for high speed line cameras. (A) Modulation and triggering scheme for collecting pump−probe spectra. Because sequential lines are processed via two different ADCs onboard the camera, their differing noise characteristics must be averaged together for pumpon and pump-off spectra. (B) Illustration of improved dynamic range achieved through averaging. For case I, each individual measurement (gray bars) is binned by the ADC to have an amplitude represented by bit n. Therefore, the average value will equal bit n. In case II, however, the noise exceeds the bin amplitude. Some individual measurements will be registered as bit n, and others as n + 1. The average of the measurements will converge on the arbitrary precision amplitude, effectively increasing the dynamic range of the detector. (C) ΔT/T kinetics trace collected from a MAPbBr3 domain illustrating the detection limit of the instrument. (D) Comparison of kinetics collected using a photodiode and lock-in amplifier to that collected using line camera detection.

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However, under conditions where the signal of interest is superposed with the source of white noise of sufficient amplitude, the effective bit depth of an ADC can be increased by making multiple measurements and averaging them together.24,25 An illustration of this effect is shown in panel B of Figure 7. Each gray bar in the figure represents the amplitude of an individual measurement. If the noise amplitude is less than the minimum resolution of the ADC (case I), then every measurement is registered as bit n. However, if the noise amplitude is larger (case II), then some measurements will be registered by the ADC as bit n, others as bit n + 1. The average of many such measurements, provided there is no signal drift, will converge to the arbitrary precision, actual amplitude. We note that while the noise in our apparatus certainly meets the criterion of sufficient, noise can be artificially added (e.g., by dithering the pump amplitude) to achieve the same effect. The reader is referred to refs22,23 for further details of convergence, optimal number of samples, and optimal noise level.

Erik M. Grumstrup: 0000-0002-0568-3889 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work supported by the Arnold and Mabel Beckman Foundation through the Beckman Young Investigator Program.

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3. CONCLUSIONS We have designed a broadband, low noise pump−probe microscope utilizing new detection technology and demonstrated its use probing the microscopic electronic properties of materials in a variety of operational modes. While careful selection and design of optical elements is necessary to ensure spectral and spatial information accurately reflects the spectroscopic response of the sample, we anticipate that broadband PPM will be a valuable tool for tying microscale material structures to specific photophysical phenomena. The low noise floor of the instrument (10−5 to 10−6) should prove to be valuable in studying a wide variety of systems, especially delicate materials where photo- or thermal-damage is a concern. Further improvements in S/N and imaging speed are easily foreseen as high-speed detectors reach line rates on par with the repetition rates of common ultrafast laser systems (≥1 MHz).

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