Double Sideband Suppressed Carrier Research Articles

High-accuracy optical vector network analyzer for optical notch and bandpass responses

A high-accuracy optical vector network analyzer (OVNA) based on optical carrier-suppressed double sideband (CS-DSB) modulation is proposed and experimentally demonstrated. The ±1st-order sideband signals are generated by CS-DSB modulation and then pass through the symmetric optical device under test (DUT). The band-stop or band-pass responses can be realized by detecting and processing the double frequency of the driven RF signal. Compared with the conventional symmetrical DSB-based OVNA, the measurement accuracy is improved by eliminating the errors caused by the even-order sidebands, and the complexity is reduced as the proposed method with only one step measurement can avoid the complex postprocessing. In addition, the optical carrier is aligned to the center frequency of the DUT by employing the Pound–Drever–Hall (PDH) technique, which provides stable measurement. At the same time, the limitation that the band-pass responses cannot be measured by the traditional single-sideband (SSB)-based OVNA is overcome. Additionally, accurate magnitude and phase responses of the DUT near the optical carrier can be also achieved since the proposed OVNA is optical filter-immune. The proposed method is theoretically analyzed and verified by experiment. A Fabry–Perot (FP) interferometer serves as the symmetric DUT; the band-stop responses in a frequency range of 6 GHz are obtained with a resolution of 1.2 MHz; and the band-pass responses with the range from 0 to 13 GHz offsetting the optical carrier are also obtained. The measurement time can reach up to 30 min with high stability. The proposed OVNA offers enhanced accuracy and a stable approach for applications in photonic systems and other innovations.

Microwave Frequency Dividers With Reconfigurable Fractional 2/N and 3/N Division Ratios

Two microwave photonic signal processing structures, which are capable to realise microwave frequency division with a tunable integer or non-integer division ratio, are presented. They are based on applying an input RF signal to a Mach Zehnder modulator, which is biased to generate a carrier-suppressed double sideband (DSB) or single sideband (SSB) optical signal. The carrier-suppressed DSB optical signal consists of the upper and lower 1 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">st</sup> order sidebands with a separation of two times the input RF signal frequency. The carrier of the SSB optical signal is suppressed by a fibre Bragg grating (FBG) connected to the modulator output. Hence the FBG output consists of the upper 1 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">st</sup> order and lower 2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">nd</sup> order sidebands with a separation of three times the input RF signal frequency. The carrier-suppressed DSB or SSB optical signal is injected into a semiconductor laser. The semiconductor laser is oscillated in the period-one state that generates a number of equally spaced frequency components, which are frequency locked by the injection light wave. Beating of these optical frequency components at the photodetector produces an RF signal with a frequency of 2/ <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> or 3/ <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> times the input RF signal frequency where <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> can be between 3 and 6. Hence the 2/ <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> frequency divider can realise 2/3, 1/2, 2/5 and 1/3 frequency division operation, and the 3/ <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> frequency divider can realise 3/4, 3/5 and 1/2 frequency division operation. The proposed 2/ <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> and 3/ <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> frequency dividers have a very simple structure compared to the reported photonics-based microwave frequency divider that can realise both integer and non-integer frequency divisions. The frequency division ratio can be tuned by simply adjusting the forward bias current of the semiconductor laser subject to optical injection. Experimental results demonstrate the two proposed structures can realise microwave frequency division with a tunable integer and non-integer division ratio for different input RF signal frequencies of 10 to 18 GHz, and over 60 dB output signal-to-noise ratio performance. More than 27 dB suppression in the unwanted frequency components around the frequency divided signal is also demonstrated.

A Microwave Photonics True-Time-Delay System Using Carrier Compensation Technique Based on Wavelength Division Multiplexing

A novel microwave photonic true-time-delay (TTD) system using carrier compensation technology is proposed and experimentally demonstrated. Wavelength division multiplexing combines ten lasers into a single beam. We separate one channel from the laser as a compensating carrier, and the compensation carrier is combined with the time-delayed optical signals to be detected. Meanwhile, sideband signals are amplified effectively thanks to carrier-suppressed double-sideband (CS-DSB) modulation. Therefore, the power of both the central optical carriers and sidebands is guaranteed, which produces a better beat frequency result than the TTD system without carrier compensation. The simulation results confirm that the signal amplitude has an order of magnitude improvement due to the compensation. With employing the delay fibers based on multiple-fiber Bragg gratings (MFBGs), the experimental delay and response time reach 90.160 μs and 160.80 ns. The proposed technique can find applications in time-delay beamforming of phased array antennas (PAAs).

Photonic scheme for broadband frequency response measurement of PDs.

We report a scheme to measure the broadband frequency response of photodetectors (PDs) with the capacity of self-calibration. The optical carrier at f 0 is modulated through one modulator, and this modulator is driven by a microwave signal with a fixed frequency f 1 to produce the carrier-suppressed double sideband optical signals f 0-f 1 and f 0+f 1. The frequency interval of the optical signals is 2f 1. Subsequently, the two optical signals are sent to another modulator driven by a swept microwave signal f m. Two pairs of carrier-suppressed double sideband signals with a high signal-to-noise ratio are generated. The frequencies of these signals are f 0-f 1-f m,f 0-f 1+f m, f 0+f 1-f m, and f 0+f 1+f m. After the PD under test, the frequency response can be extracted from the amplitude of the microwave signals at 2f 1, 2f 1-2f m, and 2f 1+2f m. Two PDs in our laboratory are experimentally characterized from 0.1 to 40GHz with a resolution of 100MHz. Compared with the traditional vector network analyzer swept method, the proposed method extends the measurement range from f m(max) to 2f 1+2f m(max) and has the capacity of self-calibration to eliminate the influence caused by the modulator frequency response on the measurement results.

A Spectrum-Efficient MoF Architecture for Joint Sensing and Communication in B5G Based on Polarization Interleaving and Polarization-Insensitive Filtering

The intelligentization of future society puts forward an urgent demand for high-precision sensing and ultra-high-speed wireless communications in the upcoming beyond fifth-generation (B5G) era. We propose and experimentally demonstrate a novel spectrum-efficient MMW-over-fiber (MoF) architecture for joint sensing and communication in B5G optical-wireless converged networks. The proposed MoF architecture is based on polarization interleaving and polarization-insensitive filtering. In the proposed architecture, the sensing and communication sidebands are generated simultaneously through asymmetrical single-sideband (ASSB) modulation, whereas the two local oscillator (LO) sidebands up-converting the sensing and communication signals to MMW band are obtained by carrier-suppressed double-sideband (CS-DSB) modulation. By interleaving the two sets of sidebands for sensing and communication in two orthogonal polarizations, the demand for higher bandwidth devices and the occupied spectral grid can thus be effectively reduced. The ASSB modulation eliminates the chromatic-dispersion- (CD) induced power fading for long-reach services. The polarization-insensitive filtering removes the need for complicated polarization tracking, resulting in a simple structure at the remote units (RUs) and polarization-free digital signal processing (DSP) at the user ends (UEs). Moreover, the two sets of sidebands originate from a shared laser, so frequency offset estimation (FOE) can be avoided to further reduce the complexity and power consumption of the DSP, thereby facilitating a user-friendly terminal. The experimental results show that a ±15-mm ranging accuracy at B5G MMW band for single-target detection is achieved, and a 30-cm ranging resolution for dual-target detection is also realized. Furthermore, a 23-Gbit/s error-free transmission rate at 28GHz over 5.41-km single-mode fiber (SMF) and 2-m wireless distance is successfully demonstrated without frequency offset compensation.

Constant-Envelope OFDM for Power-Efficient and Nonlinearity-Tolerant Heterodyne MMW-RoF System With Envelope Detection

The radio over fiber (RoF) system using optical heterodyne (OH) for broadband up-conversion and envelope detection (ED) for phase-noise-insensitive down-conversion stands out as a simple, robust, and cost-effective solution for exploiting the abundant bandwidth resource at the millimeter-wave (MMW) band. In this paper, we dedicate efforts to experimentally investigate such an MMW-RoF system based on the constant-envelope orthogonal frequency division multiplexing (OFDM) (CE-OFDM) technique. A critical benefit of employing CE-OFDM is its excellent tolerance to the nonlinear distortions, which are essential for the wide acceptance of analog RoF systems. Also, thanks to the analog angle modulation transforming the OFDM signal to a constant envelope signal, the carrier-suppressed double-sideband (CS-DSB) modulation can be implemented for encoding the CE-OFDM signal onto the optical carrier, leading to significant improvements in power efficiencies of both fiber and radiofrequency (RF) links. In experiments, a 60-GHz OH-ED MMW-RoF system is established, of which the distances of fiber and MMW wireless transmissions are 10 km and 1.2 m respectively. Under the case of 2-GHz 64-quadrature amplitude modulation (QAM) OFDM baseband signal, the achieved experimental results show that the proposed OH-ED MMW-RoF system outperforms its counterpart using the conventional OFDM in terms of nonlinearity insensitivity, RF and optical power efficiency enhancements (indicated by over 11.5-dB and 3.2-dB reductions in the lowest transmit RF and receive optical powers for satisfying the 8% error-vector-magnitude (EVM) limit). In addition, when the QAM order of the 2.5-GHz OFDM baseband signal reaches 256, the CS-DSB CE-OFDM scheme enables an acceptable EVM performance of 4.43%.

Photonic Generation of a Tunable Dual-Chirp Microwave Waveform

A photonic-assisted tunable dual-chirp microwave waveform generator based on optical heterodyne detection is proposed and experimentally demonstrated. In the proposed scheme, a three-electrode distributed Bragg reflector laser diode (DBR-LD) is used to generate a broadband frequency-chirped optical pulse. A stable optical fiber laser and a Mach-Zehnder modulator (MZM) are used to perform a double-sideband suppressed carrier (DSB-SC) signal. The frequency difference between the two sidebands of the DSB-SC signal is larger than the frequency chirp range of the optical pulse. By tuning the center frequency of the optical pulse equals that of the DSB-SC signal and beating the optical pulse and the DSB-SC signal at a photodetector (PD), a dual-chirp microwave waveform is generated. The center frequency of the generated waveform is tuned by adjusting the modulated frequency of the DSB-SC signal. The tunability of the bandwidth and the temporal duration are achieved by tuning the optical pulse. Experimental results show that the center frequency, the bandwidth, and the temporal duration have tuning ranges from 7 to 13 GHz, 13 to 17 GHz, and 500 ns to 50 μs, respectively. Chirp rates up to ±26 GHz/μs for the up- and down-chirp waveforms are measured in the experimental demonstration, respectively. The demonstration shows new avenues to implement high-performance dual-chirp microwave waveform generators for applications in modern radar systems with improved range-Doppler resolution.

A Microwave Photonic Converter with High in-Band Spurs Suppression Based on Microwave Pre-Upconversion

A microwave photonic converter based on microwave pre-upconversion is proposed and experimentally demonstrated. Only a single Mach–Zehnder modulator (MZM) is used in the converter system so that the complexity and bandwidth limiting of the link can be reduced. The transmitted and received signals before entering the MZM are firstly upconverted to high frequency (HF) by a microwave upconverter. The HF and local oscillator (LO) signals are combined to drive the MZM. Carrier-suppressed double-sideband (CS-DSB) modulation is introduced to the MZM for effective spectrum utilization. Then, the target signals can be obtained by photoelectric conversion and beating. Experimental results confirm that the mixing spurs including harmonics and intermodulation as well as original signals are all out of system frequency band from 0.8–18 GHz, and the in-band spurious suppression of at least 40 dBc is achieved. In addition, the spurious-free dynamic range (SFDR) reaches 86.23 dB·HZ2/3 for upconversion and 80.95 dB·HZ2/3 for downconversion. The proposed microwave photonic converter provides a wideband and high-purity alternative for the applications of radars and signal processing.

Broadband multi-frequency microwave photonic up-conversion with tunable phase shift

A broadband multi-frequency microwave photonic up-conversion scheme with a tunable phase shift is proposed and demonstrated based on a cavity-less ultrashort optical pulse source and a dual-polarization dual-parallel Mach–Zehnder modulator (DP-DPMZM). In this scheme, the intermediate-frequency (IF) signal is loaded onto the optical frequency comb from a cavity-less ultrashort pulse source via carrier-suppressed double-sideband (CS-DSB) modulation by using a DP-DPMZM and a 90° electric hybrid coupler (HC). Through mutual beating between multi-groups of optical modulation sidebands and multi-tone optical carrier at the photodetector (PD), multi-frequency up-converted microwave signals are obtained after coherent superposition. Meanwhile, the phase of the generated signals can be continuously tuned through varying the bias voltages of the DP-DPMZM. Simulation results show that the multi-frequency up-conversion is with a 3-dB operation bandwidth of 36 GHz and a phase shift tuning range over 360°. Hence, this scheme is a potential candidate to simultaneously realize broadband multi-frequency operation and generate the large-scale tunable phase shift in modern radar systems.

Amplitude and time-dependence of ultrasonic radiation force on modulation frequency computed from specular reflection contributions

Ever since the late 1970s, there has been interest in the modulated radiation pressure of double sideband suppressed carrier (DSSC) ultrasound, because the associated radiation pressure oscillates at a single low frequency. Recent research considers situations, where the radius of curvature of the illuminated objects greatly exceeds the wavelength at the implicit carrier frequency of the ultrasonic illumination [Marston et al., J. Acoust. Soc. Am. 149, 3042–3051 (2021); 150, 25–28 (2021)]. Furthermore, the objects of interest, cylinders, and spheres in water are taken to be sufficiently highly reflecting that the radiation force can be shown to be dominated by contributions associated with specular reflection. In such cases, it is helpful to geometrically analyze the amplitude and time dependence of the oscillatory radiation force for perfectly reflecting objects, where the relevant integrals of the stress projections can be carried out analytically. The results are expressed using Bessel and Struve functions. They explain how the amplitude and phase of the force depends on the DSSC modulation frequency in agreement with partial-wave-series based calculations. The approach is relevant in other situations. [Work supported by the U. S. Office of Naval Research.]

Optically assisted mm-wave-based multi-Gbps RoFSO transmission link under channel fading models

Free space optic (FSO) communication offers a supplement to optical fibre for satisfying the demand of next-generation wireless networks. This paper signifies photonic generation of a double sideband-suppressed carrier (DSB-SC)-based 60 GHz mm-wave by operating a dual-drive Mach–Zehnder modulator (DD-MZM) in the null point region. The radiofrequency (RF) carrying signal is investigated for dual-hop FSO/RF links of 500 m/50 m by taking optical links in the turbulent atmosphere.At the data rates of 1.25, 2.5, and 5 Gb/s, overall operation is evaluated in terms of bit error rate (BER) as a function of the received optical power. In our analysis, system performance under the Gamma-Gamma (ΓΓ) matches with the Lognormal (LN) model in moderate fluctuation using aperture averaging effect. The results are obtained with a maximum difference in the receiver sensitivity of ∼1 dB at BER = 10−6 between ΓΓ and LN models.

Photonics-Assisted Frequency Conversion and Self-Interference Cancellation for In-Band Full-Duplex Communication

A photonics-assisted frequency conversion and self-interference cancellation approach is proposed and experimentally demonstrated for in-band full-duplex (IBFD) communication. Carrier suppressed single sidebands (CS-SSB) of the intermediate frequency (IF) signal and the local oscillator (LO) signal are simultaneously obtained through the X-DPMZM in a dual-polarization dual-parallel Mach-Zehnder (DP-DPMZM) modulator. A transmit signal with high purity is produced, and a shared LO optical sideband is also provided for the subsequent downconversion. The carrier suppressed double sideband (CS-DSB) modulation for the signal of interest (SOI) is achieved via the Y-DPMZM. The self-interference signal is suppressed by adjusting the bias voltage of its main MZM. An optical bandpass filter (OBPF) is combined to realize frequency downconversion. The experimental results show that the spurious-free dynamic range (SFDR <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sub> ) is 102.6 dB/Hz <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2/3</sup> for frequency upconversion, a cancellation depth of more than 50 dB for single-frequency self-interference cancellation (SIC), and more than 22 dB for wideband SIC. The proposed link has superiority in multifunctionality, including in-band transmission, reception, and self-interference cancellation, with a shared LO.

Broadband instantaneous multi-frequency measurement based on chirped pulse compression

A broadband instantaneous multi-frequency measurement system based on chirped pulse compression, which potentially has a sub-megahertz (MHz) accuracy and a hundred-gigahertz (GHz) measurement range, is demonstrated. A signal-under-test (SUT) is converted into a carrier-suppressed double-sideband (CS-DSB) signal, which is then combined with an optical linearly frequency-modulated signal having the sweeping range covering the +1st-order sideband of the CS-DSB signal. With photodetection, low-pass filtering, and pulse compression, accurate frequencies of the SUT are obtained via locating the correlation peaks. In the experiment, single- and multi-frequency measurements with a measurement range from 3 to 18 GHz and a measurement accuracy of <±100 MHz are achieved.

Photonic full-range phase shifter with simultaneous tunable frequency multiplying capability based on a DMZM

In this paper, a novel microwave photonic full-range phase shifter with simultaneous frequency-multiplying capability is proposed. The main device is a dual-drive Mach–Zehnder modulator (DMZM) embedded in a Sagnac loop. Under the assistance of two electrical phase shifters (EPS) and a following polarizer (Pol), the optical carrier is eliminated with desired phase tunable carrier-suppressed double-sideband (CS-DSB) signal reserved. So after photoelectric conversion, the frequency-multiplied phase tunable signals are generated. The frequency multiplication factor (FMF) switching and phase tuning operation of multiplied signals can be achieved easily by adjusting the corresponding EPS. The simulation results show that the proposed structure driven by a 10 GHz RF signal can generate a frequency-doubled signal (20 GHz) or frequency-quadrupled signal (40 GHz) that features full-phase tunable range and flat power response. What is more, the proposed phase shifter has a relatively good robustness to the non-ideal factors, large frequency operation range and good frequency tunable capability.

Photonic generation of background-free frequency-doubled phase-coded microwave pulses with immunity to periodic power fading.

A novel (to the best of our knowledge) photonic approach for the generation of background-free frequency-doubled phase-coded microwave pulses with immunity to periodic power fading is proposed. By switching between the carrier suppressed double sideband (CS-DSB) modulation with reverse quadrature phase difference and carrier suppressed single sideband (CS-SSB) modulation, background-free phase-coded microwave pulses with frequency doubling of the local oscillator signal can be obtained. Thanks to the CS-DSB/CS-SSB modulation, the generated microwave pulses can be directly transmitted via single-mode fiber (SMF) without the influence of the periodic power fading. Since no filter is utilized, the proposed scheme owns a wide frequency tunable range. An experiment is conducted to verify the proposed approach. Two 1 Gbit/s phase-coded microwave pulses with center frequencies of 6 and 12 GHz are generated and successfully transmitted through a 25 km SMF. The pulse compression ratio and main-to-sidelobe ratio after the transmissions are measured as 13 and 8.84 dB, respectively.

Stable RF transfer over a fiber-optic ring with DSBCS modulation and a DSB RF signal

We propose a radio frequency (RF) transfer technique with passive phase noise compensation over a fiber-optic ring. By adopting different frequencies and same wavelength transmission and double sideband (DSB) with carrier suppression (DSBCS) modulation, the impact of backscattering can be effectively suppressed. A stable RF signal can be obtained via frequency mixing at an arbitrary access site along the fiber-optic ring. As the two directional transmissions adopt the same fiber and same wavelength from the same laser, the bidirectional propagation symmetry can be maximally guaranteed. We experimentally demonstrate 2 GHz RF signal transfer along a 100 km standard single-mode fiber-optic ring.

Ultra wideband measurement for arbitrary spectral response using double sideband modulation and low-frequency detection

An ultra-wideband measurement for arbitrary optical magnitude response is proposed and experimentally demonstrated by using optical carrier-suppressed double sideband modulation and fixed low-frequency detection. Compared with previous optical single sideband modulation-based methods, the proposed scheme doubles the measurement range. Moreover, the response can be detected at a fixed low frequency by incorporating microwave photonic frequency down-conversion. The proposed approach has the merit of measuring arbitrary response avoiding high-speed and wideband detectors. To verify the concept, simulation and experiment are carried out. The magnitude responses of two fiber Bragg gratings, which have bandwidths of 19.8 GHz and 67 GHz, are characterized with a resolution of 10 MHz by using a 43.5 GHz microwave signal source.

Revised architecture for automatic modulation recognition

Cognition and adaptability is a prominent aspect of Communication Intelligence (COMINT). Automatic Modulation Recognition (AMR) is one such aspect. AMR focuses on identifying modulation technique used at a particular carrier frequency which is got by spectral analysis (SA). The article deals with modulation recognition using feature based approach. This article addresses recognition of modulations both analog and digital sets. Analog modulations considered are Amplitude Modulation (AM), Frequency Modulation (FM), Phase Modulation (PM), Single Side Band Modulation (SSB) and Double Side Band Suppressed Carrier (DSB-SC). Digital modulations considered include Shift Keyings namely Amplitude Shift Keying (ASK), Frequency Shift Keying (FSK), Phase Shift Keying (PSK) with two and four symbols addressed as ASK2, ASK4, FSK2 , FSK4, PSK2, PSK4, respectively. Apart from this Quadrature Amplitude Modulation (QAM) with 8 symbols (QAM8) and Vestigial Side Band Modulation (VSB) stand as contenders for recognition. Its presumed that knowledge of carrier frequency,data rate and bandwidth of information is available with the recognizer; which might be extracted from SA. Analytic signal is built out of the intercepted signal frames and then Instantaneous Amplitude and Phase (IAP) is extracted from the signal frames. Statistical features are extracted from IAP. Intercepted signal frames are constructed using large sampling time, in other way considering large number of symbols in a frame which are used for threshold fixation for decision making. Finally a decision tree is designed and accuracy of the same is tested across varying modulations and noise levels.

Broadband two‐thirds photonic microwave frequency divider

A broadband two-thirds frequency divider based on two cascaded carrier-suppressed double sideband (CS-DSB) modulators is proposed and experimentally demonstrated. The first CS-DSB modulator is aimed to introduce an RF signal under frequency division to the system, and the second one is employed in an optoelectronic oscillator (OEO) loop to avoid the OEO from free running. By mixing the injection frequency and the oscillation frequency in the OEO loop, oscillation of a signal with its frequency equal to two-thirds of the injection frequency is established. An experiment is carried out, RF signals with frequencies from 12.3 to 17.7 GHz are successfully divided into 8.2 to 11.8 GHz. The maximum power ripple is 2.79 dB and the harmonic components suppression ratio is larger than 36.13 dB.

Study on eigenstate of OTF theory

The eigenstate of the Optical Transfer Function (OTF) theory is cosine fringe. In the non-Fourier transform OTF theory, the emission field of the cosine fringe is decomposed into an ensemble of interference pairs. In this paper, we use the interference theory of light to study the parameters of the two light beams of the interference pair. Afterward, we discuss the reflection coefficient of the cosine fringe and obtain the conclusion that the cosine fringe is a complex number. In addition, we analyze the interaction which is between illumination light and cosine fringe to obtain the state of the surface wave and its emission field, which reveals the mechanism of cosine fringe emission interference pairs. Furthermore, by comparing the interaction between illumination light and cosine fringe with communication modulation theory, we confirm that the principle of cosine fringe emission interference pairs is the same as that of Double-sideband suppressed-carrier. Finally, the optical imaging is analyzed by using the concept of photon ensemble, and come to the conclusion that ideal imaging does not exist. The work of this paper not only provides a basis for the non-Fourier transform OTF theory, but also contributes the illumination design of optical imaging systems.