scispace - formally typeset
Search or ask a question

Showing papers in "Optics Express in 2009"


Journal ArticleDOI
TL;DR: A parallel Monte Carlo algorithm accelerated by graphics processing units (GPU) for modeling time-resolved photon migration in arbitrary 3D turbid media renders the GPU-based Monte Carlo simulation a practical solution for data analysis in a wide range of diffuse optical imaging applications, such as human brain or small-animal imaging.
Abstract: We report a parallel Monte Carlo algorithm accelerated by graphics processing units (GPU) for modeling time-resolved photon migration in arbitrary 3D turbid media. By taking advantage of the massively parallel threads and low-memory latency, this algorithm allows many photons to be simulated simultaneously in a GPU. To further improve the computational efficiency, we explored two parallel random number generators (RNG), including a floating-point-only RNG based on a chaotic lattice. An efficient scheme for boundary reflection was implemented, along with the functions for time-resolved imaging. For a homogeneous semi-infinite medium, good agreement was observed between the simulation output and the analytical solution from the diffusion theory. The code was implemented with CUDA programming language, and benchmarked under various parameters, such as thread number, selection of RNG and memory access pattern. With a low-cost graphics card, this algorithm has demonstrated an acceleration ratio above 300 when using 1792 parallel threads over conventional CPU computation. The acceleration ratio drops to 75 when using atomic operations. These results render the GPU-based Monte Carlo simulation a practical solution for data analysis in a wide range of diffuse optical imaging applications, such as human brain or small-animal imaging.

778 citations


Journal ArticleDOI
TL;DR: Lasing in Metal-Insulator-Metal waveguides filled with electrically pumped semiconductor cores, with core width dimensions below the diffraction limit is demonstrated, showing that losses in sub-wavelength MIM waveguide can be overcome to create small plasmon mode lasers at wavelengths near 1500 nm.
Abstract: We demonstrate lasing in Metal-Insulator-Metal (MIM) waveguides filled with electrically pumped semiconductor cores, with core width dimensions below the diffraction limit. Furthermore these waveguides propagate a transverse magnetic (TM0) or so called gap plasmon mode [1-4]. Hence we show that losses in sub-wavelength MIM waveguides can be overcome to create small plasmon mode lasers at wavelengths near 1500nm. We also give results showing room temperature lasing in MIM waveguides, with approximately 310nm wide semiconductor cores which propagate a transverse electric mode.

590 citations


Journal ArticleDOI
TL;DR: A unified theoretical model of the resolution of SPR sensors is reported which makes it possible to predict the ultimate performance of all major configurations ofspr sensors, indicating that the best state-of-art SPR sensors are approaching their theoretical limits.
Abstract: We report on a unified theoretical model of the resolution of SPR sensors which makes it possible to predict the ultimate performance of all major configurations of SPR sensors. The theory indicates that the performance of SPR sensors is independent of the method of excitation of surface plasmons (prism or grating coupling) or the method of modulation (amplitude, angular or wavelength) and depends dominantly on the noise properties of the light source and detector. Results of the theoretical analysis are compared with the performance reported for several SPR sensors to illustrate that the best state-of-art SPR sensors are approaching their theoretical limits. Possibilities for further advances in the performance of SPR sensor technology are discussed.

573 citations


Journal ArticleDOI
TL;DR: A fast, powerful and stable filter based on combined wavelet and Fourier analysis for the elimination of horizontal or vertical stripes in images is presented and compared with other types of destriping filters.
Abstract: A fast, powerful and stable filter based on combined wavelet and Fourier analysis for the elimination of horizontal or vertical stripes in images is presented and compared with other types of destriping filters. Strict separation between artifacts and original features allowing both, suppression of the unwanted structures and high degree of preservation of the original image information is endeavoured. The results are validated by visual assessments, as well as by quantitative estimation of the image energy loss. The capabilities and the performance of the filter are tested on a number of case studies related to applications in tomographic imaging. The case studies include (i) suppression of waterfall artifacts in electron microscopy images based on focussed ion beam nanotomography, (ii) removal of different types of ring artifacts in synchrotron based X-ray microtomography and (iii) suppression of horizontal stripe artifacts from phase projections in grating interferometry.

570 citations


Journal ArticleDOI
TL;DR: The theoretical investigation shows that the present hybrid plasmonic waveguide with a metal cap on a silicon-on-insulator rib (or slab) has a low loss and consequently a relatively long propagation distance.
Abstract: A hybrid plasmonic waveguide with a metal cap on a silicon-on-insulator rib (or slab) is presented. There is a low-index material nano-layer between the Si layer and the metal layer. The field enhancement in the nano-layer provides a nano-scale confinement of the optical field (e.g., 50nm × 5nm) when operates at the optical wavelength λ = 1550nm. The theoretical investigation also shows that the present hybrid plasmonic waveguide has a low loss and consequently a relatively long propagation distance (on the order of several tens of λ).

523 citations


Journal ArticleDOI
TL;DR: In this paper, an Ag split ring resonator (SRR) is patterned with e-beam lithography onto planar VO_2 and etched via reactive ion etching to yield Ag/VO_2 hybrid SRRs.
Abstract: Engineering metamaterials with tunable resonances from mid-infrared to near-infrared wavelengths could have far-reaching consequences for chip based optical devices, active filters, modulators, and sensors. Utilizing the metal-insulator phase transition in vanadium oxide (VO_2), we demonstrate frequency-tunable metamaterials in the near-IR range, from 1.5 - 5 microns. Arrays of Ag split ring resonators (SRRs) are patterned with e-beam lithography onto planar VO_2 and etched via reactive ion etching to yield Ag/VO_2 hybrid SRRs. FTIR reflection data and FDTD simulation results show the resonant peak position red shifts upon heating above the phase transition temperature. We also show that, by including coupling elements in the design of these hybrid Ag/VO_2 bi-layer structures, we can achieve resonant peak position tuning of up to 110 nm.

511 citations


Journal ArticleDOI
TL;DR: The quantitative refractive index map can potentially serve as an intrinsic assay to provide the molecular concentrations without the addition of exogenous agents and also to provide a method for studying the light scattering properties of single cells.
Abstract: We report the experimental implementation of optical diffraction tomography for quantitative 3D mapping of refractive index in live biological cells. Using a heterodyne Mach-Zehnder interferometer, we record complex field images of light transmitted through a sample with varying directions of illumination. To quantitatively reconstruct the 3D map of complex refractive index in live cells, we apply optical diffraction tomography based on the Rytov approximation. In this way, the effect of diffraction is taken into account in the reconstruction process and diffraction-free high resolution 3D images are obtained throughout the entire sample volume. The quantitative refractive index map can potentially serve as an intrinsic assay to provide the molecular concentrations without the addition of exogenous agents and also to provide a method for studying the light scattering properties of single cells.

508 citations


Journal ArticleDOI
TL;DR: The maximal two-photon fluorescence microscopy (TPM) imaging depth achieved with 775-nm excitation is compared to that achieved with 1280- nm excitation through in vivo and ex vivo TPM of fluorescently-labeled blood vessels in mouse brain.
Abstract: We compare the maximal two-photon fluorescence microscopy (TPM) imaging depth achieved with 775-nm excitation to that achieved with 1280-nm excitation through in vivo and ex vivo TPM of fluorescently-labeled blood vessels in mouse brain. We achieved high contrast imaging of blood vessels at approximately twice the depth with 1280-nm excitation as with 775-nm excitation. An imaging depth of 1 mm can be achieved in in vivo imaging of adult mouse brains at 1280 nm with approximately 1-nJ pulse energy at the sample surface. Blood flow speed measurements at a depth of 900 µm are performed.

505 citations


Journal ArticleDOI
TL;DR: A high-speed silicon optical modulator with a low V(pp) (peak-to-peak driving voltage) and ultralow energy consumption based on a microring resonator, with the refractive index modulation achieved by electric-field-induced carrier depletion in a reverse-biased lateral pn diode embedded in the ring structure.
Abstract: We present a high-speed silicon optical modulator with a low Vpp (peak-to-peak driving voltage) and ultralow energy consumption based on a microring resonator, with the refractive index modulation achieved by electric-field-induced carrier depletion in a reverse-biased lateral pn diode embedded in the ring structure. With a Vpp of 2 V, we demonstrate a silicon modulator with a 3 dB bandwidth of 11 GHz, a modulation depth of 6.5 dB together with an insertion loss of 2 dB, ultralow energy consumption of 50 fJ per bit, and a small device active area of ~1000 µm2.

463 citations


Journal ArticleDOI
TL;DR: In this article, an erbium-doped fiber laser passively mode-locked with atomic layer graphene was used to generate large energy pulses with single pulse energy up to 7.3 nJ and pulse width of 415 fs.
Abstract: We report on large energy pulse generation in an erbium-doped fiber laser passively mode-locked with atomic layer graphene. Stable mode locked pulses with single pulse energy up to 7.3 nJ and pulse width of 415 fs have been directly generated from the laser. Our results show that atomic layer graphene could be a promising saturable absorber for large energy mode locking.

452 citations


Journal ArticleDOI
TL;DR: Diffraction limited images of living COS-7 cells are presented, with a particular focus on the membrane and organelle dynamics.
Abstract: Phase imaging with a high-resolution wavefront sensor is considered. This is based on a quadriwave lateral shearing interferometer mounted on a non-modified transmission white-light microscope. The measurement technology is explained both in the scope of wave optics and geometrical optics in order to discuss its implementation on a conventional microscope. In particular we consider the effect of a non spatially coherent source on the phase-image signal-to-noise ratio. Precise measurements of the phase-shift introduced by microscopic beads or giant unilamellar vesicles validate the principle and show the accuracy of the methods. Diffraction limited images of living COS-7 cells are then presented, with a particular focus on the membrane and organelle dynamics.

Journal ArticleDOI
TL;DR: A compact pin Ge photodetector is integrated in submicron SOI rib waveguide using butt coupling configuration which is sufficient to totally absorb light at the wavelength of 1.55 microm.
Abstract: A compact pin Ge photodetector is integrated in submicron SOI rib waveguide. The detector length is reduced down to 15 μm using butt coupling configuration which is sufficient to totally absorb light at the wavelength of 1.55 μm. A -3 dB bandwidth of 42 GHz has been measured at a 4V reverse bias with a responsivity as high as 1 A/W at the wavelength of 1.55 μm and a low dark current density of 60 mA/cm2. At a wavelength of 1.52 μm, a responsivity of 1 A/W is obtained under -0.5 V bias. The process is fully compatible with CMOS technology.

Journal ArticleDOI
TL;DR: The results indicate that both TPS and TPI can be used to distinguish between healthy adipose breast tissue, healthy fibrous breast tissue and breast cancer due to the differences in the fundamental optical properties.
Abstract: The complex refractive indices of freshly excised healthy breast tissue and breast cancers collected from 20 patients were measured in the range of 0.15 – 2.0 THz using a portable terahertz pulsed transmission spectrometer. Histology was performed to classify the tissue samples as healthy adipose tissue, healthy fibrous breast tissue, or breast cancers. The average complex refractive index was determined for each group and it was found that samples containing cancer had a higher refractive index and absorption coefficient. The terahertz properties of the tissues were also used to simulate the impulse response functions expected when imaging breast tissue in a reflection geometry as in terahertz pulsed imaging (TPI). Our results indicate that both TPS and TPI can be used to distinguish between healthy adipose breast tissue, healthy fibrous breast tissue and breast cancer due to the differences in the fundamental optical properties.

Journal ArticleDOI
TL;DR: The transfer matrix method is used to calculate the optical absorptance of vertically-aligned silicon nanowire (SiNW) arrays and shows that an optimized SiNW array with lattice constant of 600 nm and wire diameter of 540 nm has a 72% higher ultimate efficiency than a Si thin film of equal thickness.
Abstract: In this paper, we use the transfer matrix method to calculate the optical absorptance of vertically-aligned silicon nanowire (SiNW) arrays. For fixed filling ratio, significant optical absorption enhancement occurs when the lattice constant is increased from 100 nm to 600 nm. The enhancement arises from an increase in field concentration within the nanowire as well as excitation of guided resonance modes. We quantify the absorption enhancement in terms of ultimate efficiency. Results show that an optimized SiNW array with lattice constant of 600 nm and wire diameter of 540 nm has a 72.4% higher ultimate efficiency than a Si thin film of equal thickness. The enhancement effect can be maintained over a large range of incidence angles.

Journal ArticleDOI
TL;DR: Numerical simulations of the onset phase of continuous wave supercontinuum generation from modulation instability show that the structure of the field as it develops can be interpreted in terms of the properties of Akhmediev Breathers.
Abstract: Numerical simulations of the onset phase of continuous wave supercontinuum generation from modulation instability show that the structure of the field as it develops can be interpreted in terms of the properties of Akhmediev Breathers. Numerical and analytical results are compared with experimental measurements of spectral broadening in photonic crystal fiber using nanosecond pulses.

Journal ArticleDOI
TL;DR: Near-field, frequency-resolved characterization with high spatial resolution of the amplitude and phase of the modal structure proves that the fiber is single-moded over a wide frequency range, and the authors see the onset of higher-order modes at high frequencies as well as indication of microporous guiding at low frequencies and high porosity of the fiber.
Abstract: We report on a new class of polymer photonic crystal fibers for low-loss guidance of THz radiation. The use of the cyclic olefin copolymer Topas, in combination with advanced fabrication technology, results in bendable THz fibers with unprecedented low loss and low material dispersion in the THz regime.We demonstrate experimentally how the dispersion may be engineered by fabricating both high- and low-dispersion fibers with zero-dispersion frequency in the regime 0.5-0.6 THz. Near-field, frequencyresolved characterization with high spatial resolution of the amplitude and phase of the modal structure proves that the fiber is single-moded over a wide frequency range, and we see the onset of higher-order modes at high frequencies as well as indication of microporous guiding at low frequencies and high porosity of the fiber. Transmission spectroscopy demonstrates low-loss propagation (< 0.1 dB/cm loss at 0.6 THz) over a wide frequency range.

Journal ArticleDOI
TL;DR: It is shown that, under a suitable light concentration condition, and with a reasonable area ratio between the emitter and absorber, a STPV system employing such absorber-emitter pair and a single-junction solar cell can attain efficiency that exceeds the Shockley-Queisser limit.
Abstract: We present theoretical considerations as well as detailed numerical design of absorber and emitter for Solar Thermophotovoltaics (STPV) applications. The absorber, consisting of an array of tungsten pyramids, was designed to provide near-unity absorptivity over all solar wavelengths for a wide angular range, enabling it to absorb light effectively from solar sources regardless of concentration. The emitter, a tungsten slab with Si/SiO(2) multilayer stack, provides a sharp emissivity peak at the solar cell band-gap while suppressing emission at lower frequencies. We show that, under a suitable light concentration condition, and with a reasonable area ratio between the emitter and absorber, a STPV system employing such absorber-emitter pair and a single-junction solar cell can attain efficiency that exceeds the Shockley-Queisser limit.

Journal ArticleDOI
TL;DR: A novel method is proposed for simulating free-space propagation by limiting the bandwidth of the propagation field and also expands the region in which exact fields can be calculated by the AS.
Abstract: A novel method is proposed for simulating free-space propagation. This method is an improvement of the angular spectrum method (AS). The AS does not include any approximation of the propagation distance, because the formula thereof is derived directly from the Rayleigh-Sommerfeld equation. However, the AS is not an all-round method, because it produces severe numerical errors due to a sampling problem of the transfer function even in Fresnel regions. The proposed method resolves this problem by limiting the bandwidth of the propagation field and also expands the region in which exact fields can be calculated by the AS. A discussion on the validity of limiting the bandwidth is also presented.

Journal ArticleDOI
TL;DR: A generalised full vectorial model of nonlinear pulse propagation is reported and it is demonstrated that, unlike the standard pulse propagation formulation, the z-component of guided modes plays a key role for these new structures, and results in generalised definitions of the nonlinear coefficient gamma, Aeff, and mode orthognality.
Abstract: The propagation of pulses through waveguides with sub-wavelength features, inhomogeneous transverse structure, and high index contrast cannot be described accurately using existing models in the presence of nonlinear effects. Here we report the development of a generalised full vectorial model of nonlinear pulse propagation and demonstrate that, unlike the standard pulse propagation formulation, the z-component of guided modes plays a key role for these new structures, and results in generalised definitions of the nonlinear coefficient gamma, Aeff , and mode orthognality. While new definitions reduce to standard definitions in some limits, significant differences are predicted, including a factor of approximately 2 higher value for gamma, for emerging waveguides and microstructured fibers.

Journal ArticleDOI
TL;DR: High confinement, low-loss silicon nitride ring resonators with intrinsic quality factor (Q) of 3*10(6) operating in the telecommunication C-band with low scattering and absorption losses are demonstrated.
Abstract: We demonstrate high confinement, low-loss silicon nitride ring resonators with intrinsic quality factor (Q) of 3∗106 operating in the telecommunication C-band. We measure the scattering and absorption losses to be below 0.065dB/cm and 0.055dB/cm, respectively.

Journal ArticleDOI
TL;DR: It is shown that apart from the conventional dissipative Soliton operation, an all-normal-dispersion fiber laser can also emit square-profile dissipative solitons whose energy could increase to a very large value without pulse breaking.
Abstract: We report on the generation of 281.2 nJ mode locked pulses directly from an erbium-doped fiber laser mode-locked with the nonlinear polarization rotation technique. We show that apart from the conventional dissipative soliton operation, an all-normal-dispersion fiber laser can also emit square-profile dissipative solitons whose energy could increase to a very large value without pulse breaking.

Journal ArticleDOI
TL;DR: NeAREst, an algorithm for estimating the instantaneous three-dimensional spatio-spectral data cube from CASSI's two-dimensional array of encoded and compressed measurements is described.
Abstract: We have previously reported on coded aperture snapshot spectral imagers (CASSI) that can capture a full frame spectral image in a snapshot. Here we describe the use of CASSI for spectral imaging of a dynamic scene at video rate. We describe significant advances in the design of the optical system, system calibration procedures and reconstruction method. The new optical system uses a double Amici prism to achieve an in-line, direct view configuration, resulting in a substantial improvement in image quality. We describe NeAREst, an algorithm for estimating the instantaneous three-dimensional spatio-spectral data cube from CASSI’s two-dimensional array of encoded and compressed measurements. We utilize CASSI’s snapshot ability to demonstrate a spectral image video of multi-colored candles with live flames captured at 30 frames per second.

Journal ArticleDOI
TL;DR: Directional couplers are characterized--the key functional elements of photonic quantum circuits--and it is found that they perform as well as lithographically produced waveguide devices.
Abstract: We report photonic quantum circuits created using an ultrafast laser processing technique that is rapid, requires no lithographic mask and can be used to create three-dimensional networks of waveguide devices. We have characterized directional couplers—the key functional elements of photonic quantum circuits—and found that they perform as well as lithographically produced waveguide devices. We further demonstrate high-performance interferometers and an important multi-photon quantum interference phenomenon for the first time in integrated optics. This direct-write approach will enable the rapid development of sophisticated quantum optical circuits and their scaling into three-dimensions.

Journal ArticleDOI
TL;DR: The first investigation of photon pair generation in silicon waveguides in a continuous regime is presented, characterized by coincidence measurements, and the presence of unexpected noise is uncovered.
Abstract: Silicon waveguides are promising χ3-based photon pair sources. Demonstrations so far have been based on picosecond pulsed lasers. Here, we present the first investigation of photon pair generation in silicon waveguides in a continuous regime. The source is characterized by coincidence measurements. We uncover the presence of unexpected noise which had not been noticed in earlier experiments. Subsequently, we present advances towards integration of the photon pair source with other components on the chip. This is demonstrated by photon pair generation in a Sagnac loop interferometer and inside a micro-ring cavity. Comparison with the straight waveguide shows that these are promising avenues for improving the source. In particular photon pair generation in the micro-ring cavity yields a source with a spectral width of approximately 150 pm resulting in a spectral brightness increased by more than 2 orders of magnitude.

Journal ArticleDOI
TL;DR: It is theoretically show that the shot-noise-limited sensitivity of stimulated Raman scattering (SRS) microscopy, which enables high-contrast vibrational imaging, is similar to that of coherent anti-Stokes Raman scatter microscopy.
Abstract: We theoretically show that the shot-noise-limited sensitivity of stimulated Raman scattering (SRS) microscopy, which enables high-contrast vibrational imaging, is similar to that of coherent anti-Stokes Raman scattering microscopy. We experimentally confirm that the sensitivity of our SRS microscope is lower than the shot-noise limit only by <15 dB, which indicates that the high-sensitivity of SRS microscopy is readily available.

Journal ArticleDOI
TL;DR: Athermal silicon ring resonators are experimentally demonstrated by overlaying a polymer cladding on narrowed silicon wires with wavelength temperature dependence reduced to less than 5 pm/degrees C, almost eleven times less than that of normal silicon waveguides.
Abstract: Athermal silicon ring resonators are experimentally demonstrated by overlaying a polymer cladding on narrowed silicon wires. The ideal width to achieve athermal condition for the TE mode of 220 nm-height SOI waveguides is found to be around 350 nm. After overlaying a polymer layer, the wavelength temperature dependence of the silicon ring resonator is reduced to less than 5 pm/degrees C, almost eleven times less than that of normal silicon waveguides. The optical loss of a 350-nm bent waveguide (with a radius of 15 microm) is extracted from the ring transmission spectrum. The scattering loss is reduced to an acceptable level of about 50 dB/cm after overlaying a polymer cladding.

Journal ArticleDOI
Qin Zhang1, Xuguang Huang1, Xianshi Lin1, Jin Tao1, Xiao Ping Jin1 
TL;DR: A novel subwavelength surface plasmon polaritons optical filter based on an incompletely directional coupler is proposed and numerically simulated by using the finite difference time domain method with perfectly matched layer absorbing boundary condition to verify the feasibility of the concept of the new filter structure.
Abstract: A novel subwavelength surface plasmon polaritons optical filter based on an incompletely directional coupler is proposed and numerically simulated by using the finite difference time domain method with perfectly matched layer absorbing boundary condition. An analytical solution for the resonant condition of the structure is derived by means of the cavity theory. Both analytical and simulative results reveal that the resonant wavelengths are proportional to the length of the slit segment, inversely proportional to the antinode number of a standing wave in the segment, and are related to the slit width and the gap between the two slits. The analytical solution being consistent with the numerical simulation verifies the feasibility of the concept of the new filter structure.

Journal ArticleDOI
TL;DR: A novel method that realizes simultaneous and completely discriminative measurement of strain and temperature using one piece of Panda-type polarization-maintaining fibre is presented and it is found that the Brillouin frequency shift and the birefringence have the same signs for strain-dependence but opposite signs for temperature-Dependence.
Abstract: This paper presents a novel method that realizes simultaneous and completely discriminative measurement of strain and temperature using one piece of Panda-type polarization-maintaining fibre. Two independent optical parameters in the fiber, the Brillouin frequency shift and the birefringence, are measured by evaluating the spectrum of stimulated Brillouin scattering (SBS) and that of the dynamic acoustic grating generated in SBS to get two independent responses to strain and temperature. We found that the Brillouin frequency shift and the birefringence have the same signs for strain-dependence but opposite signs for temperature-dependence. In experiment, the birefringence in the PMF is characterized with a precision of approximately 10(-8) by detecting the diffraction spectrum of the dynamic acoustic grating. A reproducible accuracy of discriminating strain and temperature as fine as 3 micro-strains and 0.08 degrees Celsius is demonstrated.

Journal ArticleDOI
TL;DR: Testing of the zone plate with the full-field transmission x-ray microscope, XM-1, in Berkeley, showed that the lens clearly resolved 12 nm lines and spaces, a significant step towards 10 nm resolution and beyond.
Abstract: To extend soft x-ray microscopy to a resolution of order 10 nm or better, we developed a new nanofabrication process for Fresnel zone plate lenses. The new process, based on the double patterning technique, has enabled us to fabricate high quality gold zone plates with 12 nm outer zones. Testing of the zone plate with the full-field transmission x-ray microscope, XM-1, in Berkeley, showed that the lens clearly resolved 12 nm lines and spaces. This result represents a significant step towards 10 nm resolution and beyond.

Journal ArticleDOI
TL;DR: An ultra-broadband Mach-Zehnder based optical switch in silicon, electrically driven through carrier injection, with low power consumption and fast switching time is presented.
Abstract: We present an ultra-broadband Mach-Zehnder based optical switch in silicon, electrically driven through carrier injection. Crosstalk levels lower than -17dB are obtained for both the ‘on’ and ‘off’ switching states over an optical bandwidth of 110nm, owing to the implementation of broadband 50% couplers. Full 2×2 switching functionality is demonstrated, with low power consumption (~3mW) and a fast switching time (<4ns). The utilization of standard CMOS metallization results in a low drive voltage (~1V) and a record-low VπL (~0.06V·mm). The wide optical bandwidth is maintained for temperature variations up to 30K.