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In this paper we present a system for intraocular distance measurement of the human eye in vivo with high sensitivity. The instrument is based on Fourier domain low coherence interferometry (FD-LCI). Stateof-the-art FD-LCI systems are limited to a depth range of only a few mm, because the depth range is determined by the spectral resolution of the spectrometer. To measure larger distances (e.g. human eye length) we implemented two separate reference arms with different arm lengths into the interferometer. Each reference arm length corresponds to a different depth position within the sample (e.g. cornea and retina). Therefore two different depth sections, each with a depth range of a few mm can be imaged simultaneously. With the new system axial distances could be measured with a precision of 8µm. We demonstrate the performance of the instrument by measuring the axial eye length of 9 patients with cataract and compare our results with those obtained using the IOL Master (Carl Zeiss Meditec Inc.).
©2008 Optical Society of America
1. Introduction
Precise measurements of the axial eye length are required in cataract surgery and other lensreplacement procedures. Because of its low axial resolution and the need for mechanical contact between the transducer and the eye with the risk of infection the ultrasonography technique is not a preferred clinical solution. Since its approval by the US-FDA the low coherence interferometry [1–4] based Zeiss IOL Master has widely been used for that purpose [5,6]. However, several patients, especially those having rather advanced cataract could not be measured using this optical biometry method. Since the IOL Master is based on time-domain low coherence interferometry, a substantial improvement should be obtained when using Fourier-domain (FD) low coherence interferometry (LCI).
Fourier-domain low coherence interferometry has first been described and compared with time-domain LCI by Fercher et al. [4,7]. Later, a substantial sensitivity advantage of the related Fourier-domain LCI based optical coherence tomography (OCT) technique with respect to time-domain based OCT (TD-OCT) has been demonstrated [8–10]. However, in TD-OCT systems the extension of the path delay unit limits the maximum achievable imaging depth of field. Contrarily, in FD-OCT systems the depth range zmax is limited by the spectrometer resolution and can be calculated via z max=Λ 0 2/(4.δΛ) [8,9], where Λ 0 denotes the central wavelength and δΛ the spectral resolution, respectively. Typical imaging depth ranges of state-of-the-art FD-OCT instruments are in the range of 1 to 3mm, which is not sufficient for measuring the depth of the anterior chamber or the axial eye length. However, in most FDOCT spectrometers the spectral resolution is limited by the number of pixels of the line CCD array.
There are several ways how to increase depth range like using a detector with higher pixel number, different optical design of the spectrometer, or generating the full complex signal [11]. A dual reference arm configuration is an extension of a common interferometer setup and can be used to modify (increase) the depth range as well. A similar concept has been adopted in time domain low coherence reflectometry for simultaneous en-face imaging of two layers in the human retina [12] or for increasing the ranging depth in optical frequency domain imaging utilizing frequency encoding [13].
In this paper we present a FD-LCI method with an extended length measurement range capable of in vivo axial length measurement of the human eye. Two separate reference arms are used for detection of interfaces that are separated larger then the depth range determined by the spectrometer. Motion artifacts are successfully suppressed due to a high acquisition speed and axial distances are measured with a precision of 8µm. The proposed method provides important sensitivity and acquisition speed enhancements in comparison with commercially available time-domain LCI based systems. The system performance was tested on 9 patients with cataract and the results are compared with those obtained with the IOL Master. Our system was able to measure the length of the eye of cataract patients even if the IOL Master failed due to a low signal-to-noise ratio. The presented FD system has a high potential to be used clinically for biometric eye length measurements before cataract surgery.
2. Experimental setup
The optical scheme of the biometric FD-LCI system is shown in Fig. 1. A Michelson interferometer is illuminated by a superluminescent diode (SLD, SUPERLUM) with a central wavelength Λ 0=832nm and a spectral width of ΔΛ FWHM=17nm, providing an axial (depth) resolution of ~18µm in air. The full spectral width covered by the spectrometer is ΔΛ Spec=68nm and the FD-LCI depth range measured in air is 2.7mm.
Fig. 1. Schematic of FD-LCI system with 2 reference arms. SLD, superluminescent diode (Λ 0=832nm); FBC1, FBC2, fiber collimators (f=9mm); FBC3, fiber collimator (f=100mm); NPBS1, NPBS2, non-polarizing beam splitters (50:50); NDF, neutral density filter, RM1, RM2, reference mirrors; S, sample; TG, transmission grating (1200lines/mm); L1, imaging lens (f=150mm); CCD1, line scan camera.
Light emitted from the SLD pigtail is collimated with the fiber coupler FBC1 (f=9mm). The collimated 2mm diameter beam is split by a non-polarizing beam splitter (NPBS1) into sample and reference beams. The beam in the reference arm is further split by a second nonpolarizing beam splitter (NPBS2) into two separate reference beams. Thus the optical path length of each reference arm depends on the position of the reference mirrors RM1 and RM2 (each mounted on a separate translation stage) and can be adjusted independently. Therefore a signal arises from the interference between light reflected at a particular location within the sample (e.g. front surface, cornea) and at reference mirror RM1 whereas a second signal arises from the interference between light reflected at another location within the sample (e.g. back surface, retina) and at the second reference mirror RM2. Both signals are measured simultaneously with one line CCD array camera. The axial length measurement range of the system is limited only by the travel range of the used translation stages carrying the reference mirrors. The beam in the common reference arm is attenuated by the neutral density filter (NDF) in order to keep the total intensity from the reference arm slightly below the saturation of the CCD detector. The dynamic range of the spectrometer is shared for both depth sections and a 50:50 splitting ratio of NPBS2 leads to a 3dB sensitivity drop for each detected channel.
The LCI-spectrum is recorded by the spectrometer comprising the fiber coupler FBC3 (f=100mm), the volume phase holographic transmission grating (1200 lines/mm; designed for 800nm), imaging lens L1 (f=150mm) and a 12bit CCD line camera with 2048 pixels (ATMEL AVIIVA), working at 20kHz (free run mode) with an exposure time of 50µs per single acquisition.
The polarizer is used for the alignment procedure of the patient head. Together with another polarizer connected to the array CCD camera used for observing the eye position (separate camera, not shown in Fig. 1), which acts as an analyzer, one can attenuate the signal from the examined subject and therefore protect the CCD from saturation and observe the position where the beam enters the eye.
Due to the rather narrow spectral FWHM of the SLD, it is not necessary to compensate for the dispersion mismatch between sample and reference arms. At an exposure time of 50µs and 640µW power on the sample, the measured sensitivity close to the zero delay position is 95dB (for each detected signal) with a decay of 13dB as one approaches 80% of the maximal depth range.
2.1 Extended length measurement
Distances larger than the FD-LCI depth range of our system are measured by using two separate reference arms enabling independent access to two separated sample ranges. Each reference mirror is mounted on a precise (manual) micrometer translation stage (travel distance 25.000±0.001mm). A calibration of the relative position between both reference arms is necessary for precise length measurement. This calibration requires the alignment of the reference mirrors RM1 and RM2 to a position with zero optical path difference between both reference arms. During this alignment procedure the sample arm was blocked and the interference of light from both reference arms is observed. The position of RM1 defines an arbitrary zero position and RM2 is moved until the peak of the low coherence interferogram of the two reference beams is at zero delay position. One can also set this position by increasing the corresponding interference fringe period at the line camera to “infinity” (no fringes, flat spectrum). For the length measurement RM1 is kept fixed (estimated position of the cornea) while RM2 is moved by the distance of the approximate optical eye length from this zero delay position (to the estimated position of the retina). The reference offset ΔL ref is then defined as the offset of RM2 from zero delay position. The maximum theoretically detectable optical distance is 2 times the travel range of the translation stage (50mm) plus 2 times the spectrometer depth range (positive and negative frequencies).
A preliminary length measurement was performed on a d=10.114±0.001mm thick glass plate (BK7 with refractive index of 1.5257 at 830nm) - [cf. Fig. 2(a)]. The glass plate was attached to a x-y translation stage with a transparent adhesive tape. Reference mirror RM1 is used for detecting the front surface and RM2 for the back surface of the sample.
Two separate interferometric signals are overlapped on the CCD detector and detected simultaneously yielding a composite A-scan signal. Figure 2(b) shows the two overlapping Ascans after rescaling from Λ to k space and following Fourier transform. Optical length (OL) is calculated as an absolute optical path delay between mirrors RM1 and RM2 (reference offset) plus the distance between the peak position of the coherence function representing the first surface of the sample and the peak position of the coherence function representing the second surface (layer) of the sample within the relevant A-scan. OL can by expressed by OL=ΔL ref+(P FS - P BS), where ΔL ref is the reference offset, P FS and P BS represent the peak positions of the front surface and back surface of the object under test, respectively. For conversion from OL to geometrical length (GL) we used a group refractive index of 1.5257.
An advantage of our technique is that one can detect both signals close to zero path delay where sensitivity is maximal by changing the positions of the translation stages of RM1 and RM2.
Fig. 2. (a). Sample- glass plate, d=10.114± 0.001mm, (b). A-scan of the glass sample. The reference offset is 14.490mm.
To further increase the sensitivity of the system, m LCI-spectra are recorded and the resulting A-scans (after Fourier-transformation and calculation of the modulus) are averaged to form a composite A-scan. This improves the sensitivity by a factor up to √m. With the ATMEL Aviiva CCD camera a maximum of 2048 A-scans can be recorded with approximately 86% duty cycle (this limit is set by the buffer size of the camera). Note that for averaging no motion artifacts in depth should be present within the data set or these artifacts should be removed by realigning each A-scan using the corneal surface peak.
2.2 Accuracy and resolution
The accuracy of the optical length measurement depends on the calibration of the instrument whereas the precision depends on the stability of interferometer and sample. Length resolution (readout of the length) depends on the detection precision of the center of the signal peak which is influenced by the coherence length. The calibration can be done with a precision given by the axial resolution of the translation stages in the reference arms (±1µm) and the detection precision of the interference signal peak position. Since the center of the peak can be determined within the axial resolution of the spectrometer (±1.28µm/pix), the total error that results will not exceed ±2.30µm (allowing for 2 translation stages and 2x peak detection). The precision of the system was verified by 10 repeated measurements and repeated alignments of the sample or subject under test for each measurement within 5 minutes. The first set of measurements was performed on a calibrated cuvette with an air gap of 20mm. The standard deviation in this case was 2.9µm. The second set of measurements was carried out on the left eye of a healthy volunteer in vivo and yielded a standard deviation of 7.9µm.
Table 1 shows relevant parameters of the designed FD-LCI system and the comparison with the IOL Master.
Table 1. Parameters of the FD-LCI system compared with IOL Master supplied with multimode lased diode (MMLD)
For similar depth ranges the FD-LCI system operates 100 times faster and provides 4.5 times higher axial readout resolution than the IOL Master. The precision of FD-LCI is approximately 4 times better for the optical length of the eye in vivo and approximately 3.5 times better for the axial length measurement of the test sample.
3. Results
The system was tested on 9 patients with cataract. The eyes under measurement were illuminated with an incident power of 640µW which is safe for continuous illumination according to eye safety standards [14]. Each measurement includes several recordings where each data file consists of typically 100 A-scans which can be averaged on demand. The average measurement including alignment procedure for both eyes took around 5 minutes (depending on the cooperation of the patient) and was found to be convenient even for elderly patients. An example of an A-scan of a normal human eye in vivo is shown in Fig. 3.
Fig. 3. Composite A-scan of healthy human eye in vivo. The retina is located close to the origin of the graph and the front surface of the cornea further away. Both structures have a negative frequency sign but reverse order. The posterior surface of the cornea is located at the end of the depth range (not visible (below the noise floor) due to highest sensitivity decay in this region).
The head of the patient was positioned in a way to bring the retinal structures close to path length zero to take advantage from a higher sensitivity in this region. The translation stage of mirror RM1 was subsequently adjusted for the cornea. Due to the high reflectivity of the front surface of the cornea, the corneal peak can be seen along the whole depth range, but it is rather sensitive to eye motions. However, if the patient fixates the examining beam a strong backreflected signal from the cornea is observed as long as the apex is placed within the beam diameter.
Influence of transversal eye motion on the position of the detected corneal peak is eliminated by the geometry of the illumination beam and detection unit [15]. The diameter of the parallel illumination beam was 2mm. A larger beam diameter will lead to even more tolerance to transversal eye motion but will also cause decreased detection sensitivity. Appearance of the corneal peak (40–50dB above the noise level for the central reflex) was investigated on a model eye by moving the x-y translation stages where the model eye was attached. A signal drop of less than 3dB was observed for transversal motions within ±200µm. For motion artifacts of more than ±800µm the corneal signal was reduced by a factor > 10. During patient measurement, the correct eye position was monitored with an additional CCD camera.
The precision of the FD-LCI system for in vivo optical eye length (OL) measurements, defined as the standard deviation of consecutive measurements, was determined to be approximately 8µm. This includes eye length changes due to the pulsatile component of choroidal blood flow, which are of the order of a few µm [16]. OL is then converted to the geometrical length (GL) by a method that is based on Gullstrand’s schematic eye [17] and uses group refractive indices of the eye media for the corresponding wavelength (830nm) [3,18]. The IOL Master uses a different schematic model, hence for direct comparison, the measured data had to be recalculated. From both equations mentioned above we have derived the following formula for the difference of the geometrical lengths: Δ GL=GL FD-LCI -GL IOL=1.1298 - 0.0353*GL IOL. Most of the eye lengths are between 23mm and 24mm, corresponding to a difference between 318µm and 283µm, respectively. Length measurement data of the patient eyes and comparison with IOL Master data are shown in Tab. 2. The calculation of the axial eye length for the FD-LCI system was semi-automated. Within the Ascan, areas containing the required peaks (cornea, RPE) were manually selected via cursors, and the exact peak positions were automatically detected by the LabVIEW peak detect algorithm.
Table 2. Measurements of the human eye length in vivo with the FD-LCI system and with IOL Master
Table 2 shows the difference of the lengths measured with the two instruments as well as the signal to noise ratio (SNR) which was observed during the measurements. SNR was measured between the peak of the RPE and noise floor. The higher values of SNR of the FD-system show a sensitivity gain with the FD-LCI technique.
The correlation between data measured with FD-LCI and (TD-) IOL Master, respectively, is very good with a correlation coefficient r=0.998. To confirm the good agreement between the systems, a Bland-Altmann plot showing the difference between the systems against their mean is shown in Fig. 4.
Fig. 4. Bland-Altmann plot: agreement of axial length measurement between data measured with the FD-LCI system and (TD-) IOL Master (mean 9µm, median 11µm, standard deviation (SD) 11µm).
The statistical calculations were done excluding the left (pseudophakic) eye of patient 4 where a difference of 0.224mm was measured. The reason for this mismatch is the unknown group refractive index of the implanted intraocular lens and the unknown refractive index of the silicon oil used for filling the eye.
4. Discussion
Patients with cataract are mostly elderly people and it may be rather difficult for them to concentrate on the light spot for longer periods of time. With our fast system we were able to save a stack of data and find the correct data file out of the recorded data set during post processing. Every tested patient was measured on the first attempt without the need of repetition.
For the correct calculation of the eye length one should keep in mind the frequency signs and their corresponding structures of the signal peaks in Fourier space. Mixing of the objects placed in positive and negative frequency ranges leads to errors of the calculated eye length. Eye structures are within the same frequency range when cornea and retinal structures are moving in the same direction during head motion of the patient.
Our FD-system could resolve several layers in the retina of the human eye. Depending on the imaged area on the retina, the retinal pigment epithelium (RPE) might not be every time uniquely determined since it is not necessarily the highest peak. For illustration of the problem we demonstrate an OCT tomogram of the human retina in vivo (Fig. 5) which was measured with transversal PS-OCT system [19, 20]. A weak RPE signal can lead to erroneous eye length calculation.
Fig. 5. (a). Tomogram of the human retina in vivo; (b). A-scan along the position represented by cursor in Fig. 5 (a); 1- inner limiting membrane, 2- boundary between the inner and outer segment of photoreceptors, 3- end-tip photoreceptor layer, 4- retinal pigment epithelium, 5-choroid.
There are two possible solutions for simplifying and automating the previously used semiautomated method for detection of the RPE. The first method is based on averaging of a series of short-exposure A-scans. The corresponding intensities are added to obtain an averaged (composite) A-scan that accumulates the depth-dependent intensities (Fig. 6).
Fig. 6. Composite A-scan (200 single A-scans) of the human retina in vivo at central fovea region after averaging over whole data set. The labeling is similar as in Fig. 5.
From the anatomic structure the RPE is assumed to be the first peak in front of the choroid tail in the composite A-scan. Sensitivity is limited by the phase stability of the interferometer and sample under test. The exposure time must be short enough that motion artifacts neither lead to signal phase washout (within a single A-scan) nor to smearing out the retinal structure (within the entire exposure time) [21].
The second method of a possible improvement of RPE detection is based on the data acquisition itself. Figure 7 depicts a measured data set (M-scan), comprising 200 A-scans, of the human retina in vivo. The M-scan offers similar capabilities as a tomogram. This type of visualization of measured data can be used for a unique determination of the retinal layers without the need of a tomogram.
Fig. 7. M-scan comprising 200 A-scans of the human retina in vivo at central fovea region. The labeling is similar as in Fig. 5.
If there is a motion artifact present within the signal recording period, it is easily recognized in the M-scan image (shift of the A-scan). Hence, averaging can be limited to that part of the signal that is free of motion artifacts (selected by operator in post processing) or one can compensate the image for such motions by software. Such a digital compensation will compensate every single A-scan for the motion artifact. Digital phase stabilization algorithms can be implemented for automatic compensation of motion artifacts using the reflection from anterior surface of the cornea as a reference.
5. Conclusion
In conclusion, we have realized a FD-LCI system with an extended length measurement range capable of in vivo axial length measurement of the human eye. Two separate reference arms are used for detection of lengths larger than the depth range of the spectrometer. This method provides important sensitivity and acquisition speed enhancements in comparison with commercially available time-domain LCI based systems. Our system was able to measure all eye lengths of cataract patients out of an arbitrary sequence of 9 clinical patients with a precision of 8µm. The correlation between measurements by FD-LCI and IOL Master was excellent. Uncertainties concerning the interpretation of the different retinal layers from a single A-scan can be overcome with methods including the M-scan and composite A-scan. The designed FD system has potential to become a useful clinical method for biometric eye length measurements before cataract surgery.
Acknowledgment
The authors wish to thank Carl Zeiss Meditech A. G. for providing electronic and optical equipment as well as financial assistance for B. G.
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