Multi-pass microscopy

Abstract

Microscopy of biological specimens often requires low light levels to avoid damage. This yields images impaired by shot noise. An improved measurement accuracy at the Heisenberg limit can be achieved exploiting quantum correlations. If sample damage is the limiting resource, an equivalent limit can be reached by passing photons through a specimen multiple times sequentially. Here we use self-imaging cavities and employ a temporal post-selection scheme to present full-field multi-pass polarization and transmission micrographs with variance reductions of 4.4±0.8 dB (11.6±0.8 dB in a lossless setup) and 4.8±0.8 dB, respectively, compared with the single-pass shot-noise limit. If the accuracy is limited by the number of detected probe particles, our measurements show a variance reduction of 25.9±0.9 dB. The contrast enhancement capabilities in imaging and in diffraction studies are demonstrated with nanostructured samples and with embryonic kidney 293T cells. This approach to Heisenberg-limited microscopy does not rely on quantum state engineering.

ARTICLE

Received 14 Jun 2016 | Accepted 9 Aug 2016 | Published 27 Sep 2016

Microscopy of biological specimens often requires low light levels to avoid damage. This yields images impaired by shot noise. An improved measurement accuracy at the Heisenberg limit can be achieved exploiting quantum correlations. If sample damage is the limiting resource, an equivalent limit can be reached by passing photons through a specimen multiple times sequentially. Here we use self-imaging cavities and employ a temporal post-selection scheme to present full-eld multi-pass polarization and transmission micrographs with variance reductions of 4.40.8 dB (11.60.8 dB in a lossless setup) and 4.80.8 dB, respectively, compared with the single-pass shot-noise limit. If the accuracy is limited by the number of detected probe particles, our measurements show a variance reduction of 25.90.9 dB. The contrast enhancement capabilities in imaging and in diffraction studies are demonstrated with nanostructured samples and with embryonic kidney 293T cells. This approach to Heisenberg-limited microscopy does not rely on quantum state engineering.

DOI: 10.1038/ncomms12858 OPEN

Multi-pass microscopy

Thomas Juffmann1,*, Brannon B. Klopfer1,*, Timmo L.I. Frankort1, Philipp Haslinger2 & Mark A. Kasevich1

1 Physics Department, Stanford University, 382 Via Pueblo Mall, Stanford, California 94305, USA. 2 Department of Physics, University of CaliforniaBerkeley, 366 Le Conte Hall MS 7300, Berkeley, California 94720, USA. * These authors contributed equally to this work. Correspondence and requests for materials should be addressed to T.J. (email: mailto:[email protected]

Web End [email protected] ).

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Quantum enhanced metrology allows sub-shot noise measurements by exploiting quantum correlations between probe particles1. This has been demonstrated

in microscopy in scanning congurations applying N00N states2,3 or squeezed light4. Full-eld shadow imaging was demonstrated using entangled photons from parametric down-conversion5. Experimentally, these studies relied on postselection and the reduction in variance was o3.3 dB, mainly due to the difculties in creating the necessary correlations between the photons. On the other hand, it has also been shown that, under conditions of equivalent sample damage, a single probe particle that interacts m times sequentially with the sample can be used to reach the same (Heisenberg) noise limit, and that this represents an optimal parameter estimation strategy68. In this way a variance reduction of 410 dB was achieved in a phase-shift measurement9. Contrast enhancement in full-eld double-pass transmission microscopy was demonstrated using a phase-conjugated mirror to pass light twice through a sample10.

In the following, we generalize these techniques to full-eld multi-pass microscopy by placing a sample in a self-imaging cavity1113. The setup allows us to form an image of enhanced contrast by re-imaging a pulse of light m times onto the sample. Although continuous wave cavity-enhanced techniques have increased measurement resolution in various elds of science, recently, for example, at LIGO14 or in a scanning cavity microscope15, counting the exact number of interactions allows for a precise parameter estimation and an enhanced sensitivity also for phase shifts larger than 2p

m. At a constant number of photon sample interactions and employing a temporal postselection scheme, we show both retardance and transmission measurements with a sensitivity beyond the single-pass shot-noise limit, which we dene as the resolution obtained in our setup using only a single pass through the sample. It is limited by the shot noise on the number of detected photons. We show micrographs of nanostructured and biological samples, as well as the signal-enhancing capabilities in diffraction studies.

ResultsThe setup. Our setup is depicted in Fig. 1. A pulse of light (see Methods) is coupled into the cavity via the in-coupling mirror Mi.

Four lenses L14 form a microscope on either side of the sample. After the rst lightsample interaction, an image is formed on the out-coupling mirror Mo. Most of the light is reected back onto the sample, which is now illuminated by an image of itself. An image of enhanced contrast will then be formed on Mi and will again be reected onto the sample. This process is repeated multiple times. Every time an image is formed on Mo, a fraction of the light is out-coupled and imaged onto a gated intensied CCD (charge-coupled device) camera. The gating time of the CCD camera is much shorter than the cavity roundtrip time

(o500 ps and 2.7 ns, respectively), such that light can be postselected that interacted with the sample exactly m times.

Polarization microscopy. To demonstrate contrast enhancement and sub-shot-noise imaging, a wedged quartz-silica depolarizer is placed in the sample plane S. Every interaction with the quartz crystal leads to a position-dependent rotation of the polarization vector on the Poincar sphere. For a properly cut and oriented quartz crystal (see Methods), the detected number of photons in a cross-polarized setup is expected to be

Nm x; y Nm;0 x; y

sin2mZ x 2, where Nm,0(x, y) is the number of

photons detected without the polarization analyser Po. Z(x) is the

retardance of the sample, which is proportional to the local thickness of the wedged quartz crystal. Although on a single interaction the transmitted intensity varies slowly across the eld of view, more rapid signal oscillations are observed for m 3, 13

and 29 interactions (Fig. 2a). It is noteworthy that the ambiguity that arises from having m fringes instead of a single fringe can be resolved by acquiring images for different numbers of interactions.

For each image in Fig. 2a, a total number of Nm

Px

PyNm (x, y) 1.4 106 photons were detected. Figure 2b compares

the measured (left) and calculated (right) ratio

PyNm(x, y)/

PyNm,0(x, y), where the summation is carried out in between the dashed lines in Fig. 2a. The visibility of the intensity modulation is reduced from 0.98 after 1 interaction to 0.52 after 29 interactions. As a gure of merit (FOM) for multi-pass microscopy, we dene the reduction in variance of the retardance

measurement FOM

DZ1 DZm

2

, where DZm is the s.d. of Zm, which can be obtained from the measured s.d. of Nm(x)

PyNm(x, y)

. The FOM at Z p2 is

plotted in Fig. 2c (grey data points) and shows a variance reduction by 25.90.9 dB after 27 interactions. This is slightly lower than the theoretically expected value FOM m2 (grey line,

see Methods) due to residual birefringence of the optical setup, reections and misalignment. This variance reduction has been obtained for a constant number of detected photons. It is the relevant FOM if the accuracy of a measurement is limited by a nite detection rate, for example, due to the dead time of a detector. Assuming a low loss setup, it is also the relevant FOM if the number of detected photons is limited by either the collection and detection efciency or by the number of available probe particles.

Multi-pass microscopy also offers an advantage when the number of probe particlesample interactions has to be limited due to probe particle-induced damage. Under this constant damage condition, assuming a lossless cavity and sample, a FOM m is expected (red line, see Methods). The total number

via error propagation as DZm

2

DNmx

@Nmx

@Z

j j

2

f

f 2f

2f

f

f

m = 1 m = 5

m = 9

F

y x z

SMF L0 Pi Mi L1 L2 L3 L4 Mo Po Time

Intensity

S

Obj.

ICCD

Figure 1 | Sketch of the self-imaging cavity. A pulse of light (indicated in magenta) from a single-mode bre (SMF) is collimated and enters the self-imaging cavity through the in-coupling mirror Mi. The lenses L1 and L2 (L3 and L4, focal length f) form a microscope on the left (right) side of the sample

S. Light scattered in the sample plane is indicated in turquoise. After each interaction an image is formed on either Mi or Mo and reimaged onto the sample. At Mo, a fraction of the light is out-coupled and imaged using a microscope objective (Obj.) onto a gated camera (ICCD). Diffraction patterns can be imaged in the Fourier plane F. For polarization microscopy crossed polarizers are added (Pi and Po). The blue trace shows the integrated detected intensity as a function of delay, overlaid with simulated images corresponding to the respective intensity peaks.

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a c

b

175

1

20

5

N m/N m, 0

FOM (dB)

m=1 m=3

m=29

m

13 57 9 11 13 15 17 19 21 23 25 27 29

N m

0

m=13

0

0 1 2 3

0.6 1.2

0

5 10 15 20 25 m

x (mm)

(rad)

Figure 2 | Sub shot-noise polarization microscopy. (a) Micrographs after m 1,3,13 and 29 interactions (scale bar, 250 mm) with the quartz-silica

depolarizer. The inset data are taken without crossed polarizer and shows a dark spot, probably a piece of dust, reimaged onto itself m times. (b) The measured number of photons (normalized) per column (left) agrees well with the expected signal (right). (c) Experimental and calculated (solid lines) variance reduction in multipass microscopy for different numbers of collected photons (see text). The error bars give the s.d. of the variance (see Methods).

m=1 m=3

of detected photons now depends on the number of roundtrips Nm N1m aPo;maPo;1 ; such that the total number of interactions is independent of m. This implies an m-fold damage reduction if

DZ is kept constant. aPo,m gives the fraction of light blocked by the polarization analyser Po and is close to 0:58m.The measurements

(red data points) show a maximum variance reduction of11.60.8 dB, which is observed after 25 interactions. It is noteworthy that under the assumption of constant damage, the measurement error for a single multi-passed particle is equivalent to the error obtained in a Heisenberg-limited measurement with m entangled particles and a single pass.

Photon loss due to absorption, reection or scattering in the sample (as 1 ts 0.039 per interaction) or in the

cavity (ac 1 tc 0.189 per interaction) reduce the efciency

of multi-pass microscopy, as only a total number of Nm N1tm 1ma aPo;maPo;1 N1m aPo;maPo;1 photons will be detected for operation

at constant damage. Here, t tcts 1 a and maom is the mean

number of interactions of a photon with the sample before it is either lost or the mth interaction is reached (see Methods). Taking this into account, a maximum variance reduction of4.40.8 dB after three interactions is observed (blue data). This could be improved signicantly in an optimized setup, as the losses in the cavity optics are mainly due to the nite reectivity of the in- and out-coupling mirror, which, for this proof-of-principle experiment, were chosen to out-couple a considerable fraction of the beam intensity after every interaction.

Transmission measurements and diffraction studies. Transmission measurements can also benet from multi-passing as long as the total losses due to the sample and the cavity are small (see Methods). Measuring the optical density of a spatially homogeneous sample shows signal amplication and a variance reduction by 4.80.8 dB (Fig. 3a, again at constant damage). Owing to the photon losses in the sample and in the cavity no further decrease in variance is observed when the number of interactions is increased to beyond 7.

The imaging and contrast-enhancement capabilities of the setup are further exemplied with microfabricated grating structures and with embryonic kidney 293T cells. Figure 3b shows multi-pass (m 1, 3, 5) micrographs of a hexagonal hole

pattern in a carbon membrane. The resolution of the microscope is B5 mm due to the nite numerical aperture of the employed lenses (f 50 mm). The photon loss due to the carbon membrane

is amplied by multiple passes, which leads to a signicant contrast enhancement. This also becomes apparent in the images shown in Fig. 3c, which were taken in the Fourier plane of the

imaging optics. Although the single pass image is dominated by the diffraction pattern caused by the four-sided copper support structure of the carbon membrane, the hexagonal symmetry of the holes in the membrane becomes clearly visible after multiple interactions. In addition, for embryonic kidney 293T cells a clear contrast enhancement is observed (Fig. 3d). Although cells and other phase objects are hardly visible in single pass bright-eld

a

6

FOM

0.4

4

OD

FOM (dB)

0.2

2

0 1 3 5 7

0

m

b

m=5 tcm

0

I (a.u.)

c

0

1

I (a.u.)

0

d

tcm

I (a.u.)

Figure 3 | Contrast enhancement in absorption microscopy and diffraction. (a) Photon counting measurements of an optical density (OD) lter show a linear growth of the OD with m and a variance reduction at constant damage of up to 4.80.8 dB (see Methods). (b) Contrast enhancement in multi-pass micrographs of a micro-structured carbon membrane (normalized to tmc) as well as in the respective diffraction patterns (c) (normalized to the central peak). (d) Multi-pass micrographs of embryonic kidney 293T cells. Scale bar, 20 mm, 10 mm 1 and 20 mm for bd, respectively.

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microscopy, the outline of single cells becomes clearly visible in multi-pass microscopy images. Both absorption and phase shifts need to be taken into account in the analysis of such images and future high-resolution multi-pass microscopy studies will aim at exploring ne details in the interior of cells.

DiscussionMulti-pass microscopy is a technique for signal amplication and allows for optimal parameter estimation in the presence of noise sources that are not signicantly amplied by multi-passing (such as shot noise or read noise). For the images acquired at constant damage, the technique presented above relies on temporal post-selection of a few percent of the light that interacted with the sample. Although this degree of postselection is orders of magnitude less stringent than the postselection required in comparable N00N-state microscopy experiments, we note that there are at least two technologically feasible ways of overcoming this need for postselection: on the one hand, an optical switch could be incorporated into the cavity, which would allow for out-coupling all light at once. This could be achieved using a Pockels cell and a polarizing beam splitter. On the other hand, even without an out-coupling switch a metrological advantage can be gained, if a detector is used that records the detection time, and thus the number of interactions, of each individual photon.

Postselection free multi-pass microscopy will benet applications that are sensitive to photo-induced damage, such as live-cell microscopy16, the label-free detection of single proteins17, the detection of single molecules via their absorption18 or low damage imaging of exotic quantum states of matter19. Apart from increasing the detectability of such weak signals17,18, an improved signal-to-noise ratio would also lead to better spatial accuracy in super-resolution techniques that rely on these weak signals. Increased accuracy is also obtained if a measurement is limited by the number of detectable particles, for example, at wavelengths where there are no high-intensity light sources, or also in measurements that involve massive particles as probe particles (electron or ion microscopy, measurements involving anti-matter). Multi-pass electron microscopy especially seems worth considering, as sample damage limits the spatial resolution achieved in imaging biological specimens20,21.

Methods

Experimental setup. Two different laser systems were used for the experiments:

For the data in Fig. 3, a titanium sapphire laser was used (Venteon, 10 fs pulse width, 5 nJ per pulse, 100 MHz repetition rate, spectrally centred at l 780 nm).

The pulses are spectrally ltered (Semrock LL01-810-12.5) to reduce the effect of chromatic aberrations in the self-imaging cavity. This inevitably broadens the temporal width of the pulses; however, the pulses are still short compared with the cavity round trip time. A resonantly driven electro-optic modulator is used to reduce the laser repetition rate to 50 MHz with an extinction ratio of about 16 dB.

A lower repetition rate laser was required for the data in Fig. 2, to allow for more interactions before the advent of the consecutive laser pulse. The laser diode (783 nm) was driven with fast voltage pulses. Pulse widths o1 ns at a peak power of about 100 mW were achieved. The repetition rate was controlled using a direct digital synthesizer (Novatech 409B) and set to 25 MHz.

The alignment of the self-imaging cavity is done element by element (starting from the out-coupling mirror) by maximizing the light that is back-reected into the single mode bre.

Jones matrix representation of quartz-silica depolarizer. The quartz-silica depolarizer consists of a wedged plate of optical quartz cemented to a wedged plate of synthetic fused silica (OptoSigma DEQ 2S). The quartz crystal is cut and oriented such that it has the fast axis at a 45 angle with respect to the polarization of the incoming beam. The fused silica wedge has negligible birefringence and prevents beam deviation. The Jones matrix of the quartz crystal can be written as

J

cos Z2 i sin Z2 i sin Z2 cos Z2

, where Z is the phase retardance due to the birefringence of

the crystal. The retardance is proportional to the thickness of the crystal, which varies spatially, as the crystal is cut with a wedge angle of bB2: ZBbDxDn/l, where DnB0.009 is the difference in index of refraction of light polarized along the

fast or slow axis of the crystal. In the experiment horizontally polarized light

H

j iE0

1 0

enters the multi-pass microscope (I0 |E0|2 is the intensity of the incoming light), interacts with the quartz crystal m times and is nally projected onto the vertical polarization axis and detected. This can be written as

Idet E0

0 0 0 1

2 I0 sin2 mZ2.

Measurement error in retardance measurements. The error in retardance

measurements is obtained from error propagation as DZm

2

DN x

j j

2

cos Z2 i sin Z2 i sin Z2 cos Z2

m

1 0

. For a

constant number of detected particles the s.d. DNm Z p2

is independent of m,

whereas the slope @N Z

@Z

increases linearly with m. This leads to a

FOM

DZ DZ

2

m2, which scales with the square of the number of roundtrips. If

the number of probe particlesample interactions is to be kept constant, for a

lossless setup and sample, Nm Z p2

N Z

m and DNm x

q

N Z

m

. The slope

@N Z

@Z

would still increase linearly with m, leading to a FOM

DZ DZ

2

m. For

Z 6 p2, the setup could be adapted to reach optimal sensitivity3.

Measurement error in absorption measurements. Assume N0,m photons are used to probe the transmission of a sample. After m interactions, all photons are out-coupled from the cavity and detected with a photon counting detector. Without the sample, NwotmcN0;m photons will be detected. Uncorrelated repeti

tions of the measurement of Nwo will give a s.d. of DNwo

Nwo

p . With a partially absorptive sample in the setup, NwtmN0;m photons will be detected with a s.d. of

DNw

Nw

p . It follows that ts

and error propagation yields a s.d. of the

measured sample transmission of Dts tm

1N t 1 1t

N N

1=m

r

. We are interested in

the s.d. as a function of m at constant damage. This implies that the number of in-coupled photons N0,m will be a function of m, such that the number of absorbed photons Dm is independent of m. For a symmetric setup, in which the cavity losses are the same on both sides of the sample, we get DmN0;m

Pmi1 ticti 1s 1 ts and

Dm D1 yields NN 1 t1 t and

Dts;1

Dts;m m

s

1 t

1 1=ts

t

m 1

c

: 1

For maoo1, this yields a FOM of multi-pass absorption microscopy D

t Dt

2

1 t

m

1 1=t

m s

m

that scales linearly with m, just as it did for the retardance measurements.

When studying living samples, it might be more important to look at the damage reduction at constant s.d. (Dts,1 Dts,m, but DmaD1), which yields

D1Dm m2

1 t

1 1=ts

tm 1c 1 t

m

1 1=t

m s

2

and scales with m for maoo1.

Image acquisition and noise analysis. To assess the single-pass shot-noise limit, the spatially resolved photon counting capabilities of the ICCD camera are exploited. it is noteworthy that they are not required to benet from multipass microscopy.

For the retardance measurements in Fig. 2, the exposure is chosen such that B140 photons are detected per image. There are fewer than one dark counts per image. For each value of m, 10,000 images were acquired. This total data set, containing roughly 1.4 106 detected photons, is divided into Np 100 images,

each of them containing Nm photons, with N1 1.4 104, which were randomly picked without replacement. For each of these Np images, the FOM

DZ DZ

2

,

, is calculated and plotted in Fig. 2c. For this calculation,

the slope @N@Z is obtained from a sinusoidal t to the sum of all Np images. The above equation can be rewritten as 1N

where DZm

2

DN

j j

2

PNi1 Ni

N 2 and, as the images are independent of each other, Zi Z 1

j j

Ni

PNi1 Zi Z 2 1j jN

N

.

This allows us to calculate22 the s.d. of the variance as D DZm

r

, with m2 and m4 being the second and fourth

central moment of the distribution of values Zi Z. The s.d. of the FOM

DZ DZ

2

N 1

N m4

2

N 1

N 3

N m22

is then obtained from propagating the errors in (DZm)2 and (DZ1)2.

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The equations for the calculation of Nm that are given in the main text assume a symmetric setup, with equal loss ac on both sides of the sample plane. For the data and theory shown in Fig. 2, the asymmetry due to the unequal reectance of Mi and Mo is taken into account when calculating Nm and ma. With ai 1 ti and

ao

1 to being the total losses on the in-coupling and out-coupling side

of the sample, respectively, we get ma

Pmn1 tn 1st n=2bcot n 1=2bci and

Nm N tt tmaa , respectively. As the images in Fig. 2 are centred at Z p2,

the ratio aa 18m, with a maximum measured deviation of 0.04. For the

theoretical curves in Fig. 2c, aa 1 was assumed for even numbers of interactions,

for which aPo,m could not be determined experimentally.For the optical density measurements in Fig. 3 the process is similar. At m 1, 100

images are recorded, each with a total integration time t1. For m41, the integration time is tm t1/ma to operate at constant damage. For each image, the total number of

detected photons is integrated. The process is repeated without the sample and the

transmission ts

N N

1=m

and its variance are calculated. The error bars in Fig. 3

corresponds to the s.d. of the FOM as obtained from error propagation. For the theory curve, the asymmetry of the setup is again taken into account, which can result in kinks in the FOM between odd and even interaction numbers.

Data availability. The data that support the ndings of this study are available from the corresponding author upon request.

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Acknowledgements

We thank Gernot Neumayer for the preparation of the cell sample. P.H. thanks the Austrian Science Fund (FWF): J3680. This research is funded by the Gordon and Betty Moore Foundation, and by work supported under the Stanford Graduate Fellowship.

Author contributions

T.J., B.K., P.H. and M.K. conceived the experiment. B.K. and T.J. carried out the experiment. B.K., T.J. and M.K. analysed the data and prepared the manuscript. T.F. analysed alignment constraints for the setup.

Additional information

Competing nancial interests: The authors declare no competing nancial interests.

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