|
|
Yngvesson, K. S., Gerecht, E., Musante, C. F., Zhuang, Y., Ji, M., Goyette, T. M., et al. (1999). Low-noise HEB heterodyne receivers and focal plane arrays for the THz regime using NbN. In R. J. Hwu, & K. Wu (Eds.), Proc. SPIE (Vol. 3795, pp. 357–368). SPIE.
Abstract: We have developed prototype HEB receivers using thin film superconducting NbN devices deposited on silicon substrates. The devices are quasi-optically coupled through a silicon lens and a self-complementary log-specific toothed antenna. We measured DSB receiver noise temperatures of 500 K (13 X hf/2k) at 1.56 THz and 1,100 K (20 X hf/2k) at 2.24 THz. Noise temperatures are expected to fall further as devices and quasi-optical coupling methods are being optimized. The measured 3 dB IF conversion gain bandwidth for one device was 3 GHz, and it is estimated that the bandwidth over which the receiver noise temperature is within 3 dB of its minimum value is 6.5 GHz which is sufficient for a number of practical applications. We will discuss our latest results and give a detailed description of our prototype setup and experiments. We will also discuss our plans for developing focal plane arrays with tens of Hot Electron Bolometric mixer elements on a single silicon substrate which will make real time imaging systems in the THz region feasible.
|
|
|
|
Cherednichenko, S., Kroug, M., Merkel, H., Kollberg, E., Loudkov, D., Smirnov, K., et al. (2001). Local oscillator power requirement and saturation effects in NbN HEB mixers. In C. Iit.u.t.e of T. Jet Propulsion Laboratory (Ed.), Proc. 12th Int. Symp. Space Terahertz Technol. (pp. 273–285). San Diego, CA, USA.
Abstract: The local oscillator power required for NbN hot-electron bolometric mixers (P LO ) was investigated with respect to mixer size, critical temperature and ambient temperature. P LO can be decreased by a factor of 10 as the mixer size decreases from 4×0.4 µm 2 to 0.6×0.13 µm 2 . For the smallest volume mixer the optimal local oscillator power was found to be 15 nW. We found that for such mixer no signal compression was observed up to an input signal of 2 nW which corresponds to an equivalent input load of 20,000 K. For a constant mixer volume, reduction of T c can decrease optimal local oscillator power at least by a factor of 2 without a deterioration of the receiver noise temperature. Bath temperature was found to have minor effect on the receiver characteristics.
|
|
|
|
Huebers, H. - W., Semenov, A., Schubert, J., Gol’tsman, G. N., Voronov, B. M., Gershenzon, E. M., et al. (2000). NbN hot-electron bolometer as THz mixer for SOFIA. In R. K. Melugin, & H. - P. Roeser (Eds.), Proc. SPIE (Vol. 4014, pp. 195–202). SPIE.
Abstract: Heterodyne receivers for applications in astronomy need quantum limited sensitivity. We have investigated phonon- cooled NbN hot electron bolometric mixers in the frequency range from 0.7 THz to 5.2 THz. The devices were 3.5 nm thin films with an in-plane dimension of 1.7 X 0.2 micrometers 2 integrated in a complementary logarithmic spiral antenna. The best measured DSB receiver noise temperatures are 1300 K (0.7 THz), 2000 K (1.4 THz), 2100 K (1.6 THz), 2600 K (2.5 THz), 4000 K (3.1 THz), 5600 K (4.3 THz), and 8800 K (5.2 THz). The sensitivity fluctuation, the long term stability, and the antenna pattern were measured. The results demonstrate that this mixer is very well suited for GREAT, the German heterodyne receiver for SOFIA.
|
|
|
|
Huebers, H. - W., Semenov, A., Richter, H., Birk, M., Krocka, M., Mair, U., et al. (2003). Superconducting hot electron bolometer as mixer for far-infrared heterodyne receivers. In T. G. Phillips, & J. Zmuidzinas (Eds.), Proc. SPIE (Vol. 4855, pp. 395–401). Presented at the Society of Photo-Optical Instrumentation Engineers (SPIE) Conference, 4855. Tucson, USA: SPIE.
Abstract: Heterodyne receivers for applications in astronomy need quantum limited sensitivity. In instruments which are currently under development for SOFIA or Herschel superconducting hot electron bolometers (HEB) will be used to achieve this goal at frequencies above 1.4 THz. We present results of the development of a phonon-cooled NbN HEB mixer for GREAT, the German Receiver for Astronomy at Terahertz Frequencies, which will be flown aboard SOFIA. The mixer is a small superconducting bridge incorporated in a planar feed antenna and a hyperhemispherical lens. Mixers with logarithmic-spiral and double-slot feed antennas have been investigated with respect to their noise temperature, conversion loss, linearity and beam pattern. At 2.5 THz a double sideband noise temperature of 2200 K was achieved. The conversion loss was 17 dB. The response of the mixer was linear up to 400 K load temperature. The performance was verified by measuring an emission line of methanol at 2.5 THz. The measured linewidth is in good agreement with the linewidth deduced from pressure broadening measurements at millimeter wavelength. The results demonstrate that the NbN HEB is very well suited as a mixer for far-infrared heterodyne receivers.
|
|
|
|
Cherednichenko, S., Khosropanah, P., Adam, A., Merkel, H. F., Kollberg, E. L., Loudkov, D., et al. (2003). 1.4- to 1.7-THz NbN hot-electron bolometer mixer for the Herschel space observatory. In T. G. Phillips, & J. Zmuidzinas (Eds.), Proc. SPIE (Vol. 4855, pp. 361–370). SPIE.
Abstract: NbN hot- electron bolometer mixers have reached the level of 10hv/k in terms of the input noise temperature with the noise bandwidth of 4-6 GHz from subMM band up to 2.5 THz. In this paper we discuss the major characteristics of this kind of receiver, i.e. the gain and the noise bandwidth, the noise temperature in a wide RF band, bias regimes and optimisation of RF coupling to the quasioptical mixer. We present the status of the development of the mixer for Band 6 Low for Herschel Telescope.
|
|
|
|
Shcherbatenko, M., Lobanov, Y., Semenov, A., Kovalyuk, V., Korneev, A., Ozhegov, R., et al. (2017). Coherent detection of weak signals with superconducting nanowire single photon detector at the telecommunication wavelength. In I. Prochazka, R. Sobolewski, & R. B. James (Eds.), Proc. SPIE (Vol. 10229, 0G (1 to 12)). Spie.
Abstract: Achievement of the ultimate sensitivity along with a high spectral resolution is one of the frequently addressed problems, as the complication of the applied and fundamental scientific tasks being explored is growing up gradually. In our work, we have investigated performance of a superconducting nanowire photon-counting detector operating in the coherent mode for detection of weak signals at the telecommunication wavelength. Quantum-noise limited sensitivity of the detector was ensured by the nature of the photon-counting detection and restricted by the quantum efficiency of the detector only. Spectral resolution given by the heterodyne technique and was defined by the linewidth and stability of the Local Oscillator (LO). Response bandwidth was found to coincide with the detector’s pulse width, which, in turn, could be controlled by the nanowire length. In addition, the system noise bandwidth was shown to be governed by the electronics/lab equipment, and the detector noise bandwidth is predicted to depend on its jitter. As have been demonstrated, a very small amount of the LO power (of the order of a few picowatts down to hundreds of femtowatts) was required for sufficient detection of the test signal, and eventual optimization could lead to further reduction of the LO power required, which would perfectly suit for the foreseen development of receiver matrices and the need for detection of ultra-low signals at a level of less-than-one-photon per second.
|
|
|
|
Goltsman, G., Korneev, A., Minaeva, O., Rubtsova, I., Chulkova, G., Milostnaya, I., et al. (2005). Advanced nanostructured optical NbN single-photon detector operated at 2.0 K. In M. Razeghi, & G. J. Brown (Eds.), Proc. SPIE (Vol. 5732, pp. 520–529). Spie.
Abstract: We present our studies on quantum efficiency (QE), dark counts, and noise equivalent power (NEP) of the latest generation of nanostructured NbN superconducting single-photon detectors (SSPDs) operated at 2.0 K. Our SSPDs are based on 4 nm-thick NbN films, patterned by electron beam lithography as highly-uniform 100÷120-nm-wide meander-shaped stripes, covering the total area of 10x10 μm2 with the meander filling factor of 0.7. Advances in the fabrication process and low-temperature operation lead to QE as high as 30-40% for visible-light photons (0.56 μm wavelength)-the saturation value, limited by optical absorption of the NbN film. For 1.55 μm photons, QE was 20% and decreased exponentially with the wavelength reaching 0.02% at the 5-μm wavelength. Being operated at 2.0-K temperature the SSPDs revealed an exponential decrease of the dark count rate, what along with the high QE, resulted in the NEP as low as 5x10-21 W/Hz-1/2, the lowest value ever reported for near-infrared optical detectors. The SSPD counting rate was measured to be above 1 GHz with the pulse-to-pulse jitter below 20 ps. Our nanostructured NbN SSPDs operated at 2.0 K significantly outperform their semiconducting counterparts and find practical applications ranging from noninvasive testing of CMOS VLSI integrated circuits to ultrafast quantum communications and quantum cryptography.
|
|
|
|
Milostnaya, I., Korneev, A., Minaeva, O., Rubtsova, I., Slepneva, S., Seleznev, V., et al. (2005). Superconducting nanostructured detectors capable of single photon counting of mid-infrared optical radiation. In A. Rogalski, E. L. Dereniak, & F. F. Sizov (Eds.), Proc. SPIE (Vol. 5957, 59570A (1 to 9)). SPIE.
Abstract: We report on our progress in research and development of ultrafast superconducting single-photon detectors (SSPDs) based on ultrathin NbN nanostructures. Our SSPDs were made of the 4-nm-thick NbN films with Tc 11 K, patterned as meander-shaped, 100-nm-wide strips, and covering an area of 10×10 μm2. The detectors exploit a combined detection mechanism, where upon a single-photon absorption, a hotspot of excited electrons and redistribution of the biasing supercurrent, jointly produce a picosecond voltage transient signal across the superconducting nanostripe. The SSPDs are typically operated at 4.2 K, but their sensitivity in the infrared radiation range can be significantly improved by lowering the operating temperature from 4.2 K to 2 K. When operated at 2 K, the SSPD quantum efficiency (QE) for visible light photons reaches 30-40%, which is the saturation value limited by the optical absorption of our 4-nm-thick NbN film. With the wavelength increase of the incident photons,the QE of SSPDs decreases significantly, but even at the wavelength of 6 μm, the detector is able to count single photons and exhibits QE of about 10-2 %. The dark (false) count rate at 2 K is as low as 2x10-4 s,-1 which makes our detector essentially a background-limited sensor. The very low dark-count rate results in a noise equivalent power (NEP) below 10-18 WHz-1/2 for the mid-infrared range (6 μm). Further improvement of the SSPD performance in the mid-infrared range can be obtained by substituting NbN for another, lower-Tc materials with a narrow superconducting gap and low quasiparticles diffusivity. The use of such superconductors should shift the cutoff wavelength below 10 μm.
|
|
|
|
Slysz, W., Wegrzecki, M., Bar, J., Grabiec, P., Górska, M., Latta, C., et al. (2005). Fiber-coupled quantum-communications receiver based on two NbN superconducting single-photon detectors. In A. Rogalski, E. L. Dereniak, & F. F. Sizov (Eds.), Proc. SPIE (Vol. 5957, 59571K (1 to 10)). SPIE.
Abstract: We present the design and performance of a novel, two-channel single-photon receiver, based on two fiber-coupled NbN superconducting single-photon detectors (SSPDs). The SSPDs are nanostructured superconducting meanders covering an area of 100 μm2 and are known for ultrafast and efficient counting of single, visible-to-infrared photons. Their operation has been explained within a phenomenological hot-electron photoresponse model. Our receiver is intended for fiber-based quantum cryptography and communication systems, operational at near-infrared (NIR) telecommunication wavelengths, λ = 1.3 μm and λ = 1.55 μm. Coupling between the NbN detector and a single-mode optical fiber was achieved using a specially designed, micromechanical photoresist ring, positioned directly over the SSPD active area. The positioning accuracy of the ring was below 1 μm. The receiver with SSPDs was placed (immersed) in a standard liquid-helium transport Dewar and kept without interruption for over two months at 4.2 K. At the same time, the optical fiber inputs and electrical outputs were kept at room temperature. Our best system reached a system quantum efficiency of up to 0.3 % in the NIR radiation range, with the detector coupling efficiency of about 30 %. The response time was measured to be about 250 ps and was limited by our read-out electronics. The measured jitter was close to 35 ps. The presented performance parameters show that our NIR single photon detectors are suitable for practical quantum cryptography and for applications in quantum-correlation experiments.
|
|
|
|
Ekström, H., Kroug, M., Belitsky, V., Kollberg, E., Olsson, H., Goltsman, G., et al. (1996). Hot electron mixers for THz applications. In E. J. Rolfe, & G. Pilbratt (Eds.), Proc. 30th ESLAB (pp. 207–210).
Abstract: We have measured the noise performance of 35 A thin NbN HEB devices integrated with spiral antennas on antireflection coated silicon substrate lenses at 620 GHz. From the noise measurements we have determined a total conversion gain of the receiver of—16 dB, and an intrinsic conversion of about-10 dB. The IF bandwidth of the 35 A thick NbN devices is at least 3 GHz. The DSB receiver noise temperature is less than 1450 K. Without mismatch losses, which is possible to obtain with a shorter device, and with reduced loss from the beamsplitter, we expect to achieve a DSB receiver noise temperature of less ‘than 700 K.
|
|
|
|
Sobolewski, R., Zhang, J., Slysz, W., Pearlman, A., Verevkin, A., Lipatov, A., et al. (2003). Ultrafast superconducting single-photon optical detectors. In J. Spigulis, J. Teteris, M. Ozolinsh, & A. Lusis (Eds.), Proc. SPIE (Vol. 5123, pp. 1–11). SPIE.
Abstract: We present a new class of single-photon devices for counting of both visible and infrared photons. Our superconducting single-photon detectors (SSPDs) are characterized by the intrinsic quantum efficiency (QE) reaching up to 100%, above 10 GHz counting rate, and negligible dark counts. The detection mechanism is based on the photon-induced hotspot formation and subsequent appearance of a transient resistive barrier across an ultrathin and submicron-wide superconducting stripe. The devices are fabricated from 3.5-nm-thick NbN films and operate at 4.2 K, well below the NbN superconducting transition temperature. Various continuous and pulsed laser sources in the wavelength range from 0.4 μm up to >3 μm were implemented in our experiments, enabling us to determine the detector QE in the photon-counting mode, response time, and jitter. For our best 3.5-nm-thick, 10×10 μm2-area devices, QE was found to reach almost 100% for any wavelength shorter than about 800 nm. For longer-wavelength (infrared) radiation, QE decreased exponentially with the photon wavelength increase. Time-resolved measurements of our SSPDs showed that the system-limited detector response pulse width was below 150 ps. The system jitter was measured to be 35 ps. In terms of the counting rate, jitter, and dark counts, the NbN SSPDs significantly outperform their semiconductor counterparts. Already identifeid and implemented applications of our devices range from noninvasive testing of semiconductor VLSI circuits to free-space quantum communications and quantum cryptography.
|
|
|
|
Hoogeveen, R. W. M., Yagoubov, P. A., Maurellis, A., Koshelets, V. P., Shitov, S. V., Mair, U., et al. (2003). New cryogenic heterodyne techniques applied in TELIS: the balloonborne THz and submillimeter limb sounder for atmospheric research. In M. Strojnik (Ed.), Proc. SPIE (Vol. 5152, pp. 347–355). SPIE.
Abstract: We present a design concept for a new state-of-the-art balloon borne atmospheric monitor that will allow enhanced limb sounding of the Earth’s atmosphere within the submillimeter and far-infrared wavelength spectral range: TELIS, TErahertz and submm LImb Sounder. The instrument is being developed by a consortium of major European institutes that includes the Space Research Organization of the Netherlands (SRON), the Rutherford Appleton Laboratory (RAL) will utilize state-of-the-art superconducting heterodyne technology and is designed to be a compact, lightweight instrument cpaable of providing broad spectral coverage, high spectral resolution and long flight duration ( 24 hours duration during a single flight campaign). The combination of high sensitivity and extensive flight duration will allow evaluation of the diurnal variation of key atmospheric constitutenets sucyh as OH, HO2, ClO, BrO togehter will onger lived constituents such as O3, HCL and N2O. Furthermore, TELIS will share a common balloon platform to that of the MIPAS-B Fourier Transform Spectrometer, developed by the Institute of Meteorology and Climate research of the over an extended spectral range. The combination of the TELIS and MIPAS instruments will provide atmospheric scientists with a very powerful observational tool. TELIS will serve as a testbed for new cryogenic heterodyne detection techniques, and as such it will act as a prelude to future spaceborne instruments planned by the European Space Agency (ESA).
|
|
|
|
Okunev, O., Chulkova, G., Milostnaya, I., Antipov, A., Smirnov, K., Morozov, D., et al. (2008). Registration of infrared single photons by a two-channel receiver based on fiber-coupled superconducting single-photon detectors. In I. A. Sukhoivanov, V. A. Svich, & Y. S. Shmaliy (Eds.), Proc. SPIE (Vol. 7009, 70090V (1 to 8)). SPIE.
Abstract: Single-photon detectors (SPDs) are the foundation of all quantum communications (QC) protocols. Among different classes of SPDs currently studied, NbN superconducting SPDs (SSPDs) are established as the best devices for ultrafast counting of single photons in the infrared (IR) wavelength range. The SSPDs are nanostructured, 100 μm2 in total area, superconducting meanders, patterned by electron lithography in ultra-thin NbN films. Their operation has been explained within a phenomenological hot-electron photoresponse model. We present the design and performance of a novel, two-channel SPD receiver, based on two fiber-coupled NbN SSPDs. The receivers have been developed for fiber-based QC systems, operational at 1.3 μm and 1.55 μm telecommunication wavelengths. They operate in the temperature range from 4.2 K to 2 K, in which the NbN SSPDs exhibit their best performance. The receiver unit has been designed as a cryostat insert, placed inside a standard liquid-heliumstorage dewar. The input of the receiver consists of a pair of single-mode optical fibers, equipped with the standard FC connectors and kept at room temperature. Coupling between the SSPD and the fiber is achieved using a specially designed, precise micromechanical holder that places the fiber directly on top of the SSPD nanostructure. Our receivers achieve the quantum efficiency of up to 7% for near-IR photons, with the coupling efficiency of about 30%. The response time was measured to be < 1.5 ns and it was limited by our read-out electronics. The jitter of fiber-coupled SSPDs is < 35 ps and their dark-count rate is below 1s-1. The presented performance parameters show that our single-photon receivers are fully applicable for quantum correlation-type QC systems, including practical quantum cryptography.
|
|
|
|
Hübers, H. - W., Semenov, A., Richter, H., Birk, M., Krocka, M., Mair, U., et al. (2002). Terahertz heterodyne receiver with a hot-electron bolometer mixer. In J. Wold, & J. Davidson (Eds.), Proc. Far-IR, Sub-mm, and mm Detector Technology Workshop.
Abstract: During the past decade major advances have been made regarding low noise mixers for terahertz (THz) heterodyne receivers. State of the art hot-electron-bolometer (HEB) mixers have noise temperatures close to the quantum limit and require less than a µW power from the local oscillator (LO). The technology is now at a point where the performance of a practical receiver employing such mixer, rather than the figures of merit of the mixer itself, are of major concern. We have incorporated a phonon-cooled NbN HEB mixer in a 2.5 THz heterodyne receiver and investigated the performance of the receiver. This yields important information for the development of heterodyne receivers such as GREAT (German receiver for astronomy at THz frequencies aboard SOFIA)[1] and TELIS (Terahertz limb sounder), a balloon borne heterodyne receiver for atmospheric research [2]. Both are currently under development at DLR.
|
|
|
|
Hübers, H. - W., Semenov, A., Richter, H., Birk, M., Krocka, M., Mair, U., et al. (2002). Terahertz Heterodyn Receiver with a hot-electron bolometer mixer. In U. Wolf, J. Farhoomand, & C. R. McCreight (Eds.), Far-IR, Sub-mm & MM Detector Technology Workshop (pp. 3–24). NASA CP. NASA.
Abstract: During the past decade major advances have been made regarding low noise mixers for terahertz (THz) heterodyne receivers. State of the art hot-electron-bolometer (HEB) mixers have noise temperatures close to the quantum limit and require less than a µW power from the local oscillator (LO). The technology is now at a point where the performance of a practical receiver employing such mixer, rather than the figures of merit of the mixer itself, are of major concern. We have incorporated a phonon-cooled NbN HEB mixer in a 2.5 THz heterodyne receiver and investigated the performance of the receiver. This yields important information for the development of heterodyne receivers such as GREAT (German receiver for astronomy at THz frequencies aboard SOFIA) [1] and TELIS (Terahertz limb sounder), a balloon borne heterodyne receiver for atmospheric research [2]. Both are currently under development at DLR.
|
|
|
|
Zhang, W., Li, N., Jiang, L., Ren, Y., Yao, Q. - J., Lin, Z. - H., et al. (2008). Dependence of noise temperature of quasi-optical superconducting hot-electron bolometer mixers on bath temperature and optical-axis displacement. In C. Zhang, & X. - C. Zhang (Eds.), Proc. SPIE (Vol. 6840, 684007 (1 to 8)). Spie.
Abstract: It is known that the increase of bath temperature results in the decrease of critical current of superconducting hot-electron bolometer (HEB) mixers owing to the depression of superconductivity, thus leading to the degradation of the mixer’s sensitivity. Here we report our study on the effect of bath temperature on the heterodyne mixing performance of quasi-optical superconducting NbN HEB mixers incorporated with a two-arm log-spiral antenna. The correlation between the bath temperature, critical current, LO power requirement and noise temperature is investigated at 0.5 THz. Furthermore, the heterodyne mixing performance of quasi-optical superconducting NbN HEB mixers is examined while there is an optical-axis displacement between the center of the extended hemispherical silicon lens and the superconducting NbN HEB device, which is placed on the back of the lens. Detailed experimental results and analysis are presented.
|
|
|
|
Hubers, H. - W., Semenov, A., Richter, H., Schwarz, M., Gunther, B., Smirnov, K., et al. (2004). Heterodyne receiver for 3-5 THz with hot-electron bolometer mixer. In J. Zmuidzinas, W. S. Holland, & S. Withington (Eds.), Proc. SPIE (Vol. 5498, pp. 579–586). SPIE.
Abstract: Heterodyne receivers for applications in astronomy and planetary research need quantum limited sensitivity. In instruments which are currently build for SOFIA and Herschel superconducting hot electron bolometers (HEB) will be used to achieve this goal at frequencies above 1.4 THz. The local oscillator and the mixer are the most critical components for a heterodyne receiver operating at 3-5 THz. The design and performance of an optically pumped THz gas laser optimized for this frequency band will be presented. In order to optimize the performance for this frequency hot electron bolometer mixers with different in-plane dimensions and logarithmic-spiral feed antennas have been investigated. Their noise temperatures and beam patterns were measured. Above 3 THz the best performance was achieved with a superconducting bridge of 2.0 x 0.2 μm2 incorporated in a logarithmic spiral antenna. The DSB noise temperatures were 2700 K, 4700 K and 6400 K at 3.1 THz, 4.3 THz and 5.2 THz, respectively. The results demonstrate that the NbN HEB is very well suited as a mixer for THz heterodyne receivers up to at least 5 THz.
|
|
|
|
Baselmans, J. J. A., Hajenius, M., Gao, J., de Korte, P., Klapwijk, T. M., Voronov, B., et al. (2004). Doubling of sensitivity and bandwidth in phonon-cooled hot-electron bolometer mixers. In J. Zmuidzinas, W. S. Holland, & S. Withington (Eds.), Proc. SPIE (Vol. 5498, pp. 168–176). SPIE.
Abstract: NbN hot electron bolometer (HEB) mixers are at this moment the best heterodyne detectors for frequencies above 1 THz. However, the fabrication procedure of these devices is such that the quality of the interface between the NbN superconducting film and the contact structure is not under good control. This results in a contact resistance between the NbN bolometer and the contact pad. We compare identical bolometers, with different NbN – contact pad interfaces, coupled with a spiral antenna. We find that cleaning the NbN interface and adding a thin additional superconductor prior to the gold contact deposition improves the noise temperature and the bandwidth of the HEB mixers with more than a factor of 2. We obtain a DSB noise temperature of 950 K at 2.5 THz and a Gain bandwidth of 5-6 GHz. For use in real receiver systems we design small volume (0.15x1 micron) HEB mixers with a twin slot antenna. We find that these mixers combine good sensitivity (900 K at 1.6 THz) with low LO power requirement, which is 160 – 240 nW at the Si lens of the mixer. This value is larger than expected from the isothermal technique and the known losses in the lens by a factor of 3-3.5.
|
|
