Photon noise limit

Detectors which are photon noise-limited act as photon buckets , and collect nearly all the photons emitted from the source. In the dispersive instrument, the signal-to-noise ratio (SNR) is then easy to calculate. The signal from do is given above, while the noise is proportional to the square root of the signal, so ... 

In the photon noise limit, the photon arrival rate at the detector is described by a Poisson process, which has a variance cr = N. If the average count rate is O, then in (27) can be replaced by Vt O. In other words, the probability of false detection decreases with the square root of the measurement interval T. Figure 17 shows frequency distributions obtained from a 1 pg ml sample. The dash-dot lines are Gaussian fits to data recorded at a time interval T = 1 s, giving a TDER of 0.156. The solid lines are Gaussian fits to the data averaged over T = 8 s, giving a TDER of 0.015. 

Once the sky map reaching the system is determined, one can compute the associated photon noise that will reach the detector. The fundamental limit of any ideal photon integrating sub-mm detector is the noise associated with the Bose-Einstein Auctuations in photon arrival rate (Lamarre 1986) which results in a photon noise limited NEP... 

R. W. Boyd, Photon bunching and the photon-noise-limited performance of infrared detectors. Infrared Phys. 22(3), 157-162 (1982). ISSN 0020-0891. doi 10.1016/0020-0891(82)90034-3. http //www.sciencedirectcom/science/article/pii/0020089182900343... 

From this, the signal-to-noise ratio for photon noise limited Fourier transform spectroscopy is... 

It is therefore desirable to further decrease the photon-noise limit. At flrst, this seems to be impossible because the limit is of principal nature. However, it has been shown that under certain conditions the photon-noise limit can be overcome... 

Fig. 2.15. Photon noise limited Df at peak wavelength (assumed to be cutoff wavelength), for a photovoltaic detector for selected background temperatures Tg. Values for a cooled photoconductive detector are 0.71 times those shown. (Assumes 27t steradian field of view and >/ = 1) (after Jacobs and Sargent [2.160])...

Fig. 2.17. Relative increase in photon noise limited D and D (T) achieved by using cooled aperture in front of detector (after Kruse et al. [2.3, p. 36])... 

Electronic detectors offer the ultimate in frequency response, as high as tens of gigahertz, and especially in the visible, approach photon-counting or quantum-limited performance. As such, they offer magnitudes of improvement in sensitivity over thermal devices. In the limit of photon-counting performance, the signal measurement fluctuation or noise is produced by the random production of photo electrons. In many cases, electrical noise in the postdetection amplifier, rather than photon noise, limits the sensitivity. 

FIGURE 10 Graph of detector performance indicating mode of operation, bandwidth, and pulse response. SL, signal or photon noise limited. BL, background limited. AL, amplifier noise limited. Various semiconductors are centered at their approximate wavelength cutoff. 

The three curves for amplifier-limited operation have been calculated assuming typical amplifier normalized noise currents of 0.3,1, and 3 pA/a/Hz for the respective band-widths 1 kHz, I MHz, and I GHz. The applicable value depends upon the specifications of the chosen amplifier. Generally, the best performance is obtained by integrating the amplifier and detector on the chip. Avalanche multiplication can supply pre-amplification current gain and reduce the expected NEP by a factor from 10 to 100. At 1 GHz bandwidth, this can bring performance to within an order of magnitude of photon noise-limited behavior. 

Two techniques may be used to enhance the performance of the above detectors, yielding improved sensitivity but restricted to special applications. These are heterodyne detection and optical amplification. Both techniques approach photon-noise-limited performances but only when receiving a single diffraction-limited mode of the receiver aperture. 

Although a heterodyne system is photon-noise limited, as indicated by Eq. (27), the noise produced by the local oscillator is additive. Thus, unlike the photon counter of Section II.A, there is always a noise floor equivalent to an uncertainty of one photon per sampling time, T = B, even with zero signal. In a sense, a heterodyne or coherent system overmeasures the incoming signal by extracting... 

A typical layout of a squeezing experiment based on a Mach-Zehnder interferometer (Sect. 4.2.3) is shown in Fig. 14.64. The output of a well-stabilized laser is split into two beams, a pump beam bi and a reference beam b2. The pump beam with the frequency co] generates by nonlinear interaction with a medium (e.g., four-wave mixing or parametric interaction) new waves at frequencies o l /. After superposition with the reference beam, which acts as a local oscillator, the resulting beat spectrum is detected by the photodetectors D1 and D2 as a function of the phase difference A0, which can be controlled by a wedge in one of the interferometer arms. The difference between the two detector output signals is monitored as a function of the phase difference A0. Contrary to the situation in Fig. 14.62, the spectral noise power density p(/, 0) (= Pnep per frequency interval d/ = 1 s ) shows a periodic variation with 0. This is due to the nonlinear interaction of one of the beams with the nonlinear medium, which preserves phase relations. At certain values of 0 the noise power density Pn(/, 0) drops below the photon noise limit... 

In most cases, uy can be neglected. For very constant. sources, a a. is small. Owing to the proportionality between Ud and Id it is advisable to select a photomultiplier with a low dark current, to avoid detector noise limitations. When these points are taken care of, the photon noise limits Ihe power of detection. 

Figure 2.22 illustrates the performance of infrared detectors operating in the 1 to 1000 pm interval and the photon noise limits for cooled and uncooled detectors. The data are from a report of the National Materials Advisory Board [2.17]. Table 2.8 presents additional information concerning the detectors of Fig. 2.22, including the references from which the data were obtained. 

The photon noise is simply due to the uncertainty, a, in the number of photons per second, i.e., the detected signal level. In the photon noise limit the signal-to-noise ratio is proportional to the square root of the photon arrival rate. When the measured noise is the photon noise in the background radiation, the detection is said to have reached background limited performance (BLIP). 

Many of the parameters in Table 1 were set by requiring that the final performance in SIRTF come within a factor of 1.5 of the background photon noise limits despite the effects when cosmic rays strike the detectors. The relevant tradeoffs have been determined firom Herter (1990). 

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