Optical coherence tomography (OCT) allows the visual-ization of tissue structures with micrometer resolution.An interferometer and a low-coherence light source areused as an optical gating for photons ref lected from tis-sue structures at different depths.1 The depth gatingof the sample is done by a mechanical scanning de-vice in the reference arm of the interferometer. Theoutput of the interferometer is recorded by a detector,and the depth information is derived from the tempo-ral modulation of the signal. This approach is calledtime-domain OCT.
To avoid moving parts with all their disadvantages,the use of image sensors was proposed.2 –5 In a re-cently introduced OCT system the depth information isreconstructed from the interference pattern generatedby the superposition of two point sources, one emittingthe backscattered light from the probe and the otheremitting the reference light (Fig. 1). In the interfer-ence pattern the A-scan is coded as a spatially varyingintensity instead of a time-dependent signal. In theseso-called linear OCT (LOCT) systems the intensity inthe detector plane I �x� can be described as
IF �x� � Ip 1 IR 1 2�IPIR �1�2 �sin�k1x��g�x� . (1)
Here IP is the probe intensity; IR is the reference in-tensity; and g�x� is the amplitude of the modulation,which is determined by the degree of coherence of thelight source. From Fig. 1, spatial carrier frequencykI of the interference pattern can be calculated fromangle a enclosed by the two beams and wavelengthof the light l as �2pa��l. For a low-coherence lightsource a modulation is detected only when the opti-cal distances in both arms of the interferometer arematched. Therefore ref lections from different depthsof the sample cause local modulation at different loca-tions of the detector.
The sensitivity of an array detector for a certain spa-tial frequency is described by the modulation transferfunction (MTF). Figure 2 shows the measured5 MTF
0146-9592/04/141644-03$15.00/0
for the sensor used in our experiments. It can be seenthat the sensitivity of the sensor drops fast towardhigher frequencies and reaches zero when the periodof the modulation equals the width of one pixel.
Measurements with good contrast are thereforelimited to spatial frequencies significantly belowthe pixel frequency. If, for example, the samplingof the fringe pattern is done with two pixels perfringe period, 4Dd�l pixels are needed for a certainmeasurement depth Dd. A measurement range of2 mm at a wavelength of 830 nm requires an imagesensor with 104 pixels. Although sensors with thatmany elements are available, an OCT system utilizingthem would be rather bulky. Additionally, readoutand processing of that many data points per A-scanrequires a high bandwidth of the analog-to-digitalconverter and the successive data processing unit.
Therefore it is advantageous to reduce the frequencyof the interference pattern before sampling. Chang-ing the carrier frequency of a signal by multiplicationwith a second single frequency (mixing) is a well knownprocedure in signal processing. For intensity distri-butions IF �x� this multiplication can be performed by
Fig. 1. Principle of the LOCT: Probe and reference in-tensity interfere as planar waves on the surface of an im-age sensor.
Fig. 2. Measured MTF of the sensor and calculated MTFwith attached mask.
a mask with a periodic transmittance modulation infront of the detector.
For calculating the performance of a LOCT systemwith optical downconversion, a mask with a spatiallysinusoidal transparency function T �x� directly in frontof the image sensor was assumed:
T �x� �12
112
sin�kMx� , (2)
where kM is the spatial mask frequency. The inten-sity distribution behind mask IM is derived by multi-plication with the interference pattern from Eq. (1):
IM �x� � IF �x�T �x� . (3)
In the frequency domain the spectrum of IM is a con-volution �≠� of the spectra of IF and T :
FOU�IM �x�� � FOU�IF �x�� ≠ FOU�T �x�� . (4)
The spectra of both IF and T consist of two frequen-cies, 0 and kI or kM , respectively. When convoluted,five frequencies (0, kI , kM , kI 2 kM , and kI 1 kM )result. The spectra of the detected signal can be ob-tained by an additional multiplication with the MTF ofthe sensor. To gain a significant reduction in the car-rier frequency, kM must be chosen to be higher thanthe pixel frequency. If kI 2 kM is close to 0, it will bedetected by the image sensor, whereas the other fre-quencies from Eq. (4) are not detected because of thedecreasing sensor MTF toward higher frequencies.
The MTF of a sensor with a mask can be calcu-lated from the measured MTF and Eq. (4) (Fig. 2).Frequencies below the pixel frequency can still be de-tected, but the amplitude is halved due to the averagemask transmission of 0.5. Additionally, frequenciesaround the mask frequency yield a modulation on thesensor with a maximum amplitude of 25%. This iscaused by the shadowing effect of the mask (50%)and the fact that half of the intensity modulation istransformed into the sum frequency, where it cannotbe detected by the sensor. The average intensity andinterference contrast are reduced to 50% compared
with the direct measurement of the fringe pattern.The signal-to-noise ratio (SNR) of a shot-noise-limited LOCT system is proportional to the ratio ofthe interference amplitude and the square root ofthe average intensity5: 20 log��IP IR�1�2��IP 1 IR�1�2�.Therefore downconversion reduces the SNR by20 log��1�4��
p1�2� � 9 dB.
For the experiments a mask with a square-wavetransparency function was used. In this case a num-ber of additional terms arise from the higher orders ofthe Fourier components of the square wave, but, as be-fore, all high-frequency components are damped by theMTF of the sensor, so that the basic principle remainsunchanged.
To test this principle, we attached a custom-mademask to a complementary metal-oxide semiconductorsensor (Photon Vision Systems, LIS 1024, pixel size of8 mm 3 125 mm, 1024 pixels). The mask was manu-factured from 2-mm-thick glass plates by structuringa chromium layer on one side with an electron beam.The period of the resulting transmittance pattern was2.66 mm, which is a third of the pixel period. Af-ter structuring, the glass plates were cut into piecesof 8 mm 3 1.5 mm. The mask was glued on top ofthe image sensors after the cover window had beenremoved.
Figure 3 shows the basic optical setup of the ex-periment. The light of a superluminescent diode (Su-perlum SLD37MP, lc � 830 nm, FWHM � 45 nm) isdirected through a fiber coupler to the probe. The ref-erence wave is generated by the backref lection of thefiber tip in the probe arm. This approach has the ad-vantage that the probe and reference intensities travelthe same path from their origin to the detection unit;therefore all dispersion- and path-length-dependenteffects in the fibers are canceled out. In the detectionunit the light is partitioned by a 50% beam splitter.Both parts are focused by a cylindrical lens on thelinear image sensor. The angle between the twobeams is chosen so that kI equals 3.25 fringes�pixel.The mean path-length difference between the twobeams is equal to the path-length difference estab-lished between the probe light and the reference lightin the probe arm of the interferometer. A disad-vantage of this interferometer design is that bothbeams consist of both reference and probe light, butonly probe light ref lected from the beam splitter caninterfere with the reference light ref lected from themirror. The other components contribute only to the
Fig. 3. Schematic of the experimental setup. SLD, su-perluminescent diode.
Fig. 4. Light intensity measured by the sensor with a cov-erslip as a probe. Inset, enlargement of the second modu-lation. Because of the downconversion effect, there areonly three fringes in the FWHM of the light source.
Fig. 5. A-scan signal of Fig. 4 after bandpass f ilteringand demodulation on a logarithmic scale. The third peakat pixel 650 is caused by light ref lected back and forthwithin the coverslip.
Fig. 6. B-scan image of the threads of a screw. The im-age dimensions are 940 mm 3 2 mm at a lateral resolutionof 10 mm. The image sensor was used at a frame rate of200 Hz.
incoherent intensity offset of the system. This halvesthe interference contrast and SNR.
First measurements were done with a coverslip withan optical thickness of 140 mm and a refractive indexof 1.57. Figure 4 shows the raw data derived fromthe linear-image sensor with the mask. The Gauss-ian shape of the beam profile is modulated by low-frequency components, probably caused by interferencebetween the surface of the mask and the top side ofthe semiconductor. The two modulations caused bythe surfaces of the coverslip are visible around pix-
els 290 and 480. The interference contrast definedas the ratio between the maximum amplitude and theaverage intensity was approximately 8.5%. Accordingto Fig. 2, an interference contrast of 18% is expectedfor the experimental system when kI is adjusted to3.25 fringes�pixel. The difference might be caused bydiffraction effects of the mask. With a measured dis-tance of �6 mm between the mask and the surfaceof the sensor and a mask period of 2.6 mm, diffrac-tion arising from the mask has already spread light toneighboring pixels, decreasing the contrast.
The ratio between the standard deviation of thenoise f loor and the peak value of the coverslip signalswas calculated as 47 dB (Fig. 5). The sensitivity ofthe system, defined as the ratio between the high-est possible signal amplitude and the noise f looris �61 dB. For the calculation we consider thatthe interference amplitude of the coverslip surface isp4% � 20% of that achieved with a mirror in the probe
arm of the interferometer. Therefore the measuredsignal in Fig. 5 is 14 dB smaller than a peak causedby mirrors. The measurement range of the systemcan be determined from the distance of the two peaksto be 1.17 6 0.01 mm.
Downconversion of the fringe pattern with a maskplaced in front of the image sensor is a method fordecreasing the number of pixels for a LOCT systemby an order of magnitude. Therefore standard imagesensors can be used to implement OCT systems with ameasurement range of more than 1 mm.
Because LOCT systems consist of only a lens, twobeam splitters, and a sensor, these systems are smalland simple. For larger volumes the mask can be struc-tured within the complementary metal-oxide semicon-ductor standard process in a metal layer directly on thesemiconductor surface. The systems are also poten-tially very fast. Approximately 20,000 A-scans�s arepossible with the sensor used here. The major disad-vantage of the technique is a loss in the SNR of �9 dBcompared with time-domain OCT systems.
For applications in which a stable and simple systemwithout the ultimate dynamic range is needed, LOCTwith optical downconversion may be an interesting al-ternative to conventional OCT systems. A possible ap-plication is metrology as demonstrated by the examplein Fig. 6.
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