Supporting Material 1. Actual design in FPGA

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1 Supporting Material. Actual design in FPGA. FPGA and its peripheral circuit The circuit design was described with Verilog and developed with Xilinx ISE. The circuit was realized in a low- commercial FPGA board (Papilio Pro, Gadget Factory). This board is based on a Spartan-6 FPGA (XC6SLX9-2C, Xilinx). The internal clock 240 MHz was made by a phase locked loop (PLL) oscillator in the FPGA from a 32 MHz external oscillator on the board. A USB interface chip, FT2232D (Future Technology Devices International Ltd.), is equipped on the board, but, unfortunately, this chip can not be used because low data transfer rate. Since the transfer rate is a key issue in the recorder, a USB interface board with a faster chip, FT232H, was used (AE-FT232HL, Akizuki Denshi, Tokyo). The input signal from the detector was a 5V logic and a single fast CMOS 5V torrent logic, TC7SG34FU (Toshiba), was used as a level translator for the FPGA input. Four translators and the USB interface board were wired on a unversal board to use I/O of Papilio Pro. The construction problem will be reduced if one can use a FPGA board with a fast USB interface chip. As far as we know, there are some low Spartan-6 FPGA boards with a FT2232H USB interface chip (Saturn, Numato Systems Pvt. Ltd, Bangalore, India) or a FX2LP (CY7C6803, Cypress) USB interface chip (for exmaple, TKDN-SP6-6, Tokushudenshi, Tokyo, Japan; USB6, CESYS GmbH, Herzogenaurach, Germany). Since FT2232H (port A) is very similar to FT232H and FX2LP has more functions and a deep FIFO buffer, these board can probably be used in this recorder with some minor modifications of design. The connection is defined in the ucf file as follows: NET signals[3] LOC="P95" IOSTANDARD=LVTTL; # B9 L40P_GCLK_ NET signals[2] LOC="P8" IOSTANDARD=LVTTL; # A9 L46P_ NET signals[] LOC="P85" IOSTANDARD=LVTTL; # A L43P GCLK5 NET signals[0] LOC="P93" IOSTANDARD=LVTTL; # A3 L4P GCLK9 NET ft232_data[0] NET ft232_data[] NET ft232_data[2] NET ft232_data[3] NET ft232_data[4] NET ft232_data[5] NET ft232_data[6] NET ft232_data[7] LOC="P4" IOSTANDARD=LVTTL; # C0 L65N_0 LOC="P5" IOSTANDARD=LVTTL; # C L65P_0 LOC="P6" IOSTANDARD=LVTTL; # C2 L64N_0 LOC="P7" IOSTANDARD=LVTTL; # C3 L64P_0 LOC="P8" IOSTANDARD=LVTTL; # C4 L63N_0 LOC="P9" IOSTANDARD=LVTTL; # C5 L63P_0 LOC="P20" IOSTANDARD=LVTTL; # C6 L62N_VREF_0 LOC="P2" IOSTANDARD=LVTTL; # C7 L62P_0 NET ft232_oe_n LOC="P23" IOSTANDARD=LVTTL; # C8 L37PNGCLK2_0 NET ft232_clk LOC="P24" IOSTANDARD=LVTTL PERIOD = 6.67 ns; # C9 L37P_GCLK3_0 NET ft232_wr_n LOC="P26" IOSTANDARD=LVTTL; # C0 L36N_GCLK_0 NET ft232_rd_n LOC="P27" IOSTANDARD=LVTTL; # C L36P_GCLK_0 NET ft232_txe_n LOC="P3" IOSTANDARD=LVTTL; # C2 L35N_GCLK_0 NET ft232_rxf_n LOC="P32" IOSTANDARD=LVTTL; # C3 L35P_GCLK_0 All actual sources will be provided upon request to the author. The key codes in our concrete design were described below.

2 .2 Definition of ISERDES ISERDES2 in Spartan-6 was used in our design. ISERDES2 was programmed to work a 4-bit shift register and a input serial stream was stored in the register. The actual input, SIG, was connected to the input of ISERDES2. Clk ISERDES and Clk bin were the sampling clock 960 MHz and master clock 240 MHz, respectively. The definition of ISERDES2 and wiring are shown below: ISERDES2 #(.BITSLIP_ENABLE ("FALSE"),.DATA_RATE ("SDR"),.DATA_WIDTH (4),.INTERFACE_TYPE ("RETIMED"), // NETWORKING_PIPELINED.SERDES_MODE ("NONE")) iserdes2_master (.Q(bit_seq[3]), // old time time={t,t2,t3,t4} bit={q,q2,q3,q4}.q2(bit_seq[2]), // t4 > t.q3(bit_seq[]),.q4(bit_seq[0]), // recent time.shiftout(), // for cascading.incdec(),.valid(), // these are for phase detection mode.bitslip( b0),.ce0(ce), // Clock enable input.clk0(clk_iserdes),// IO Clock network input (the primary clock).clk( b0), // secondary IO clock network input for DDR mode.clkdiv(clk_bin), // Global clock network input. This is the clock for the fabric domain..d(sig_in_delay), // Input signal from IOB..IOCE(SERDES_STROBE), // Data strobe signal derived from BUFIO CE. Strobes data // capture for NETWORKING and NETWORKING_PIPELINES alignment modes..rst(reset), // Asynchronous reset only..shiftin(), // for Slave mode // unused connections.fabricout(),.cfb0(),.cfb(),.dfb() ); IBUF #(.IOSTANDARD ("LVTTL")) ibuf_inst0 (.I( SIG),.O(SIG_int)); assign SIG_in_delay = SIG_int; // if you insert IDELAY2, use here.3 Sampling and event detection The serial bit stream in the 4-bit register was analyzed to detect event. The initial edge of the detector signal carries the timing information of the photon arrival. Therefore, the transition of logic singal from low to high or from high to low, deping on the detector signal, was searched. The 2

3 input data stream, divided by 4 sampling times, is schematically illustrated in Fig.S. Since the transition may come the of the 4-bit register, one-more bit was used to keep the previous last bit. Then, the transition points in the 5-bit stream were detected and the positions were recoreded as event times as shown by the arrows in Fig.S. Since two bits are needed to detect the transition, the dead time of one sampling time always exists. The transition points were recorded in a two 2-bit data. The lower 2-bit, Detect, indicates the position with the coarse time resolution, when 4 sampling times was coarsen to 2 double sampling times. The higer 2-bit, DetectH, indicates the fine position in the coarse position. Therefore, each input stream was recorded in a 2-bit data and in a 4-bit data with coarse and fine time resolution (480 MHz and 960 MHz), respectively. sampling clock input stream master clock 0 transition point now 0 0 past time Detect (coarse resolution) DetectH (fine resolution) Fig.S The sampling stream and data structure. The essential part of the actual code of encoding is shown below: reg [3:0] detected; // timing of event assign Detect = detected[:0]; assign DetectH = detected[3:2]; reg keep_seq4; // last event of the previous bin // edge detect (the one of the edge timing is recorded) // timing resoultion is the half of the bin size // and encode de-serialized data (event time record) // Clk_bin) begin keep_seq4<= bit_seq[0]; // keep -bit for next bin case( {keep_seq4,bit_seq}) // if there is an inverter between the signal // and FPGA input, the following condition // should be inverted ( cond) // past <-> now old (/2) recent (/2) 5 b0000: begin detected[0] <= b0; detected[] <= b; detected[2] <= b0; detected[3] <= b; 5 b000: begin 3

4 ... skip detected[0] <= b0; detected[] <= b; detected[2] <= b0; detected[3] <= b0; 5 b00: begin detected[2] <= b; detected[3] <= b0; 5 b0: begin detected[2] <= b0; detected[3] <= b0; 5 b0000: begin detected[2] <= b0; detected[3] <= b0; 5 b000: begin detected[2] <= b; detected[3] <= b0; 5 b0000: begin detected[2] <= b; detected[3] <= b0; default: begin detected[0] <= b0; detected[] <= b0; detected[2] <= b0; detected[3] <= b0; case // All 32 patterns were encoded to 4-bits data. The absolute time running master clock (240 MHz) was also counted by 8-bit counter (not shown). In case of coarse time resolution, each 2-bit event data of 4-inputs and the 8-bit absolute time were recorded in a 6-bit data. In case of fine time resolution, each 4-bit event data of 2-inputs and the absolute time were recorded in a 6-bit data. These are shown in Fig. (b). When the absolute time counter is rolled over at each.07 µs, this is also considered as an event to be transferred to know the absolute time in the post process. For the check of inconsistency of the absolute time, another 8-bit counter was clocked by the rollover of the absolute time counter. This counter value was transferred using 8-bit event data byte when the roll over of the absolute time counter occurred but no input event. The 6-bit data was stored in a 6-bit first-in first-out (FIFO) memory, whose depth was 892. The output of the FIFO was 8-bits for the USB transceiver chip, FT232H. The chip was reading 8-bit data from the FIFO and transferred with the synchronous parallel FIFO mode of the chip. For the measurement of temporal profile, one channel is served to the reference channel. The photon counting rate is usually very low relative to the excitation rate. Therefore, if the all events 4

5 are recorded, most data does not contain the photon detection event. The excitation pulse rate is usually around an order of MHz or more. Therefore, the huge data size will mostly consume the band width of USB and waste the memory and storage. Therefore, the reference event was recorded only when the photon was detected to reduce the data size. In the actual measurements, the reference was appropriately delayed outside of the recorder to cover the time range of photon arrival and the reference event at the second channel was transferred if the photons were detected before the reference event. This is very similar to the reverse scheme of time-correlated single photon counting (TCSPC) system. TCSPC system can count only one event but this recorder can count all events associated with the one excitation pulse. This mode, temporal profile mode, was hardcoded in the FPGA and can be switched from the normal mode by a software controllable register. Currently, the temporal profile mode is passive because we aimed temporal profile measurements with this recorder with a minimum modification. However, there are two better options to ext this mode. The key of the both options is the synchronization between the master clock of the recorder and the external laser source. First option is the synchronization of master clock to the external clock source. In this case, the recorder design will become the external frequency depent because of the configuration of internal PLL oscillator to generate the master clock and seems to not be flexible. Second option is the opsite of the first option. This option is more easy and does not lose the flexibility. A programable clock generator design for the external laser source and an external interface logic circuit are only needed. This is the best option if the laser source is external triggerable. However, this option may not be good when the laser system includes a PLL feed back mechanism with some mode-locked lasers. The transfered data through USB2.0 were received with the bulk transfer mode. Two 8-bit data of the 6-bit data described above were simply transferred without any process with the synchronous parallel FIFO mode of FT232H. The program on the host computer was receiving data and keeping data in the memory not to miss the data. Thus, the memory size of the host computer is essential. The test of input maximum count rate showed the transfer of 8MHz periodic events without loss of data with a simple receiving software using libraries libftdi and libusb-.0 on a Linux system (Ubuntu 0.04) on a high PC (Precision T5400, X GHz, Dell). The 8MHz events are corresponding to 36Mbyte/sec. transfer rate and this value was very close to the specification limit rate 40Mbyte/sec. of FT232H. After all data were received in memory, then the data were recorded on the hard disk drive or processed appropriately. The control circuit was also desinged. Basically, the circuit managed the measurement mode like coarse or fine time resolution and temporal profile mode and the measurement setup like start, stop and measurement time. These were controlled by registers, whose bits modify the opration, by the software on the host computer through USB. Additionally, 4-channel frequency counters to monitor the count rate were embeded in the FPGA and the count values were transferred through the USB to serial UART chip (FT2232D) on Papilio Pro board. 5

6 2. Correlation Functions with Dynamic Light Scattering Measurements The recorder was tested by conducting a dynamic light scattering (DLS) measurements because the correlation time can be determined by the known parameters, such as wavelength, scattering angle, diameter of the scatter particle, temperature and viscosity of the solvent. A single mode laser at 785 nm was collimated and injected from one side of a cm 4-faces clear quartz cuvette in a 500 ml beaker filled water. The scattered light at 90 was detected by another collimator with a single mode fiber and guided to a multimode : fiber splitter for two single photon-counting detectors. The recorder was operated in the fine time resolution mode (.04 ns). The correlation function was calculated with the cross-correlation scheme. The samples were diluted NIST traceable latex microsphere solutions with 50, 00 and 50 nm particles in diamter. The temperature was C. Normalized g () (τ) Normalized g () (τ) τ (ms) 50nm τ (µs) Fig.S2 The normalized correlation functions of the scattering light. The correlation offset was subtracted and the amplitude was normalized to. Then, the horizontal axis was scaled by factor 2 to show the electric field correlation functions. Figure S2 shows the correlation functions (CFs) of the scattering light. The CFs almost decay as a single exponential function but the decay of the sample with the 50 nm microsphere was deviated upward at the tail. The deviation is probably due to the vibration of the optical table. The correlation function at the few nano-second region was dropped because of the dead time of the sampling (.04 ns) of the recorder. The other early part was very flat, indicating negligible radio frequency interference between the input channels. 6

7 Correlation time (ms) Diameter (nm) Fig.S3 The correlation time against the diameter of the microsphere and a linear fit of the data. Figure S3 shows the relationship between the diameter of the microsphere and the correlation time. The correlation time is proportional to the diameter and well fitted by a linear function. The slope 20.±0.5 µs/nm is very good agreement with 20.2 µs/nm calculated with the parameters as follows: wavelength 785 nm, refractive index.33, viscosity cp, temperature 296 K, the scattering angle 90. 7

8 3. Near-infrared fluorescence fluctuation system A near-infrared fluorescence fluctuation measurement system was constructed to demonstrate the application of the device. The system consists of an inverted epifluorescence microscope, an excitation source with a continuous wave (CW) laser (I0785SD000B, Innovative Photonics Solutions) at 785nm, and a homemade pulsed laser (T780P00S, Thorlabs) at 780nm driven by an avalanche pulser, and single photon counting detectors. The excitation laser was coupled to a polarization maintained single mode (PM-SM) fiber and collimated at the of the fiber to fill the aperture of an objective lens (Uplan Apo x63/water, Olympus). The fluorescence was collected by the same lens and separated from the excitation light by a dichroic mirror and an interference filter. The fluorescence was focused on an edge of a graded index multimode (GI-MM) fiber. The core of the fiber works as a confocal pinhole. A single photon counting detector was connected at the of the fiber. A : GI-MM fiber splitter was used to equally divide the detection light into two detectors for cross correlation measurements. A single photon photomultiplier tube module (H863-50, Hamamatsu) or a single photon avalanche detector (C , Hamamatsu) was selected because of the very low afterpulse characteristics. 4. Fluroescence correlation function of some near-infrared probes Figure S4 shows typical CFs with the IR806-BSA and BSA-QD solutions. The setup of the detection was cross-correlation mode to eliminate the distortion of the CF at an early time region less than 200-ns. The measurement times were 500 sec for IR806-BSA solution and 3000 sec for BSA-QD, respectively, to visualize the anti-bunching effect as described below. The CF with the BSA-QD solution shows a significant decrease at earlier than 00-ns, which is attributed to the anti-bunching effect. The excited state lifetime of this QD was about 00ns and the recovering time of the antibunching is very close to the lifetime. The CF of IR806-BSA was noisy at the early time region and the antibunching is not visible. This is probably due to very few photons dropped in a nano-second range, resulting very bad statistics in this time range. The CF was analyzed by a single component equation, G(τ) = n ( + τ/τ 0 ) ( + τ/τ 0 /s 2 ) /2 + () where n, τ 0 and s are the number of particles in the volume element defined by the confocal optics, correlation time and the structure parameter which is the ratio of the ellipsoidal shape of the focused volume, respectively [E.Elson, Biophys.J.0, 2855 (20)]. 8

9 G(τ) BSA-QD(CdSeTe/CdS) IR806-BSA Time (µs) Fig.S4 Fluorescence correlation functions of IR806- BSA and BSA-QD solutions. The correlation time is determined by ω 2 /(4D), where ω and D are the beam waist of the focused volume and the diffusion constant, respectively. The data can be fitted by the equation but the structure parameter could not be determined with a good accuracy and thus it was fixed to 5. The correlation time was strongly deping on the excitation power. The excitation power 6.4µW was chosen by the maximum power where the change of the CF became almost negligible but the fluorescence intensity was not too small. The correlation time was determined by the fitting to the above equation and the ratio of the hydrodynamic radius by the ratio of the correlation time. The correlation time of BSA-QD and IR806-BSA were 0.88-ms and 0.38-ms, respectively. Assuming the radius 3.3nm of IR806-BSA, the diameter of BSA-QD can be determined 7.7-nm, which is very good agreement with the other data, DLS and SEM. The count rate of the IR806- BSA and BSA-QD solutions were 2.6 and 3.63 kcps, respectively. The count per molecules of each solution becomes. kcps/molecule for IR806-BSA solution and.4 kcps/molecule for BSA-QD. 9