Applied physics

Brighter images with no added noise

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A special type of optical amplifier based on a vapour of rubidium has been demonstrated that makes faint images brighter without adding noise. This concept could find use in biological imaging and image processing.

Anyone who has adjusted the sensitivity settings of a camera in weak light will have noticed that increasing the electronic gain of the camera's light sensor yields images of poor quality. This observation reveals a general property of amplification of signals: it is accompanied by noise. However, there are special conditions in which such noise can be circumvented. Writing in Physical Review Letters, Corzo et al.1 describe how they have achieved this in the amplification of faint images.

In the quest to improve the accuracy of measurement and observation of a system, certain fundamental bounds exist that limit the precision with which a physical quantity can be determined. Specifically, according to Heisenberg's uncertainty principle, it is not possible to attain perfect precision in simultaneously determining a system's observable quantity and its conjugate variable; two variables, X and Y, are conjugate variables if they are related to one another through a mathematical operation known as a Fourier transform. Examples of pairs of conjugate variables include time and frequency, and position and momentum. The case in which the uncertainties ΔX and ΔY in X and Y, respectively, are equal and minimal is known as the standard quantum limit for X and Y, and a system in such a state of minimum uncertainty is said to be in a coherent state. However, because the uncertainties are not necessarily equal, measurements can be performed that have a precision beyond the standard quantum limit. Such precision can be achieved using 'squeezed' states2, in which one of the two conjugate variables has a smaller (squeezed) uncertainty than that associated with coherent states.

For light, the conjugate variables X and Y are typically taken to be the quadratures that define the light's time-varying electromagnetic field: E(t) = Xcos(2πνt) + Ysin(2πνt), where t denotes time and ν is frequency. Figure 1 shows a comparison between the electromagnetic field in a coherent state, typically that of a laser beam, and one in a squeezed state2,3. Squeezing can be produced by a nonlinear optical process called four-wave mixing, in which two photons at frequencies ν1 and ν2 are annihilated and two new photons at frequencies ν3 and ν4 are created while satisfying conservation of energy, and therefore frequency: ν1 + ν2 = ν3 + ν4. For this process to occur efficiently, another rule, known as phase matching, must apply. This states that the sum of the momenta of the interacting photons at these frequencies is conserved (that is, the sum of the propagation constants k1 + k2 = k3 + k4). The result of this interaction is that the uncertainties in the quadratures of the generated photon field become unequal, such that one is less than (squeezed) that of a coherent state and the other is greater.

Figure 1: Coherent and squeezed states.

a, Conceptual representation of a coherent state of light. X and Y represent the quadratures of the light's electromagnetic field at frequency ν: E(t) = Xcos(2πνt) + Ysin(2πνt), where t is time. The distance OA is the field's amplitude A, and the angle φ is the phase (where the field's peaks and dips lie). The size of the disk represents the uncertainties in the amplitude and phase, ΔA and Δφ, which are equal in value. The field's temporal evolution is shown on the right. b, A squeezed state, in which ΔA is smaller and Δφ larger than their coherent-state equivalents. c, A phase-squeezed state, in which Δφ is smaller and ΔA larger than their coherent-state analogues. d, In a type of field amplification known as phase-insensitive amplification, the total uncertainty (area of the disk) is amplified. e, In phase-sensitive amplification, the total uncertainty remains constant. Corzo et al.1 have applied this form of amplification to faint images.

The interaction that produces squeezing represents a special type of linear amplifier. The most common form of amplifier produces phase-insensitive amplification (PIA), in which both quadratures of the field are amplified equally. But phase-sensitive amplification (PSA), in which one quadrature is amplified while the other is de-amplified, can also be realized. In PIA, the quotient between the signal-to-noise ratio of the input field and that of the output, amplified field — the noise figure — approaches 2 for large values of the gain. By contrast, the noise figure for the PSA can be unity, independently of the value of the gain4.

The first demonstrations5,6 of noiseless amplification (that is, with no degradation of the signal-to-noise ratio of the input signal)by means of PSA were followed by a proposal to apply it to the light fields associated with faint images7, which was subsequently demonstrated experimentally8. In their study, Corzo et al. attained PSA noiseless amplification, based on four-wave mixing, of faint images in a set-up9 that had been used to demonstrate quantum entanglement between spatially extended light fields. Previous noiseless amplification of images8,10 has been achieved using certain crystals that display a nonlinear optical response when light propagates through them. The authors' image amplifier is based on an atomic vapour of rubidium that exhibits a highly nonlinear optical response owing to the 'near-resonant' nature of the interaction between the rubidium vapour and the light fields. As a result, 'pump' light beams at frequencies ν1 and ν2 do not need to be tightly focused in the amplifying medium, thereby relaxing the requirement of phase matching and allowing a larger number of image pixels to be amplified.

In Corzo and colleagues' experiment, the four-wave mixing process involves two pump fields whose frequencies (ν1 and ν2) are nearly the same as the frequencies associated with two atomic transitions in a vapour of rubidium, νge and νie. The signal to be amplified is at a frequency νS, such that ν1 + ν2 = 2νS. Unlike many four-wave-mixing experiments, spontaneous emission noise is negligible as long as ν1, ν2 and νS are sufficiently detuned from νge and νie. The authors show that, for a gain of 3.9, the noise figure remains nearly equal to unity for this PSA approach to amplifying faint images, and is well below the predicted value for an ideal (with no added noise) PIA method. What's more, they demonstrate that this amplifier can provide gain for more than 2,000 pixels, allowing the amplification of fairly complex image patterns.

The authors' PSA technique could be used in several applications, for example when a detector (camera) is either insufficiently sensitive to light or too noisy. A future path for this research would be to create amplifiers that operate in the mid- and far-infrared, or X-ray, wavelength regimes. In the X-ray regime, a PSA could reduce the exposure of biological tissues to harmful radiation. However, most of these applications would require transposing the wavelength of operation of the current demonstration to these other wavelengths. In principle, this is possible using different sets of atomic transitions and/or systems. For applications in which there is no control over the light source (such as in astronomical imaging), another issue is the frequency bandwidth of the nonlinear medium. For interactions in rubidium vapour, the frequency bandwidth over which the nonlinear interaction occurs efficiently is very narrow and must be close to the atomic-transition frequencies. This provides additional motivation to develop nonlinear materials that can operate over broad bandwidths and have a large nonlinear response.


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Correspondence to Stéphane Clemmen or Alexander Gaeta.

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Clemmen, S., Gaeta, A. Brighter images with no added noise. Nature 491, 202–203 (2012) doi:10.1038/491202a

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