Showing papers in "Sensors and Actuators A-physical in 1995"

Equivalent-circuit model of the squeezed gas film in a silicon accelerometer

Abstract: We present a new electric equivalent circuit for the forces created by a squeezed gas film between vertically moving planar surfaces. The model is realized with frequency-dependent resistors and inductors. Circuit analysis tools are applied to calculate the response of a micromechanical silicon capacitive accelerometer in both the frequency and the time domains. The simulations are shown to match the measured frequency responses in an excellent way. We utilize the circuit model to calculate the effective viscosity in a narrow gap between the moving surfaces. The results are compared with different slip-flow equations discussed in the literature. We present a simple approximate equation of the pressure-dependent viscosity that is valid for both viscous and molecular damping regions, and has 5% accuracy.

Damping characteristics of beam-shaped micro-oscillators

Abstract: The damping characteristics of beam-shaped microactuators that oscillate in the transverse direction are analytically evaluated to establish a design method that minimizes energy consumption and increases dynamic performance. The damping force due to airflow is calculated using the Navier-Stokes equation, the accuracy of which is verified by comparing the calculated damping with experimental results. The contributions to the damping due to squeeze force, internal friction, and support loss are calculated by using the Reynolds equation, structural damping theory, and a two-dimensional theory of elasticity, respectively. The final formulae, obtained in simple and closed forms for easy use in the actual design process, are then used to evaluate the relationships between the beam size and the damping ratio of silicon cantilevers, Permalloy cantilevers, and Permalloy spiral springs. Finally, the step response of a Permalloy cantilever is calculated and the relationship between beam size and settling time is determined.

A bidirectional silicon micropump

Abstract: In this paper we present a bidirectional silicon micropump. It consists of an electrostatically actuated diaphragm and two passive check valves. It differs from other well-known diaphragm pumps, generally referred to as unidirectional pumps, in the layout of the valves. We have designed a flap valve with a first mechanical resonance frequency between 1 and 2 kHz (in the fluid environment). At low actuation frequencies (0.1–800 Hz), the pump works in the forward mode. At higher frequencies (2–6 kHz) the pump operates in the reverse direction. This is due to a phase shift between the response of the valves and the pressure difference that drives the fluid. Investigating different pump layouts, we achieve maximum pump rates of 250 and 850 μl min -1 in the forward direction as well as 400 and 200 μl min -1 in the reverse direction. The maximum back pressure is 31 000 Pa (3.1 m H 2 O) in the forward and 7000 Pa (0.7 m H 2 O) in the reverse direction.

Sensors based on piezoelectric resonators

Abstract: A review of sensors based on piezoelectric crystal resonators is presented. The survey focuses on the fundamental resonator modes rather than on the variety of surrounding support configurations in special sensor applications. First, the general properties of vibrating crystal sensors and their inherent superiority are described. The sensor concepts utilizing either homogeneous resonators with temperature and pressure (stress) as primary measurants or composite resonators with areal mass density and viscoelastic properties of the 'foreign' layer as primary measurands are discriminated. A comparison between bulk acoustic wave (BAW) and surface acoustic wave (SAW) resonators with respect to their primary sensitivity functions and principal capabilities for sensor applications is given and the importance of recent investigations on Lamb wave and horizontal polarized shear wave (HPLW) interdigital transducer (IDT) resonators is acknowledged. The importance of mode purity for high dynamic range sensors based on resonators and some aspects of the demand on specialized electronics are emphasized. The present state of established sensors based on primary sensitivities, e.g., quartz-crystal thermometers, pressure transducers, thin-film thickness and deposition-rate monitors, viscoelastic layer analysers (crystal/liquid composite resonators) is reviewed. A selection of the most promising recently investigated vibrating crystal sensors utilizing indirect sensitivities is described, including the wide field of analyte-selective coatings and resonator-based immunosensors or immunoassays. Finally, the potential of alternative piezoelectric materials for future sensor developments is briefly discussed.

A valve-less planar fluid pump with two pump chambers

Abstract: A new planar fluid pump based on the valve-less diffuser/nozzle pump principle is presented. The pump consists of two pump chambers, each with two flow rectifying diffuser/nozzle elements with rectangular cross sections, one at the inlet and one at the outlet. The pump chambers are arranged in parallel for high pump flow. Each pump chamber has two piezoelectrically vibrated diaphragms. The planar pump is fabricated in brass with a total thickness of 1 mm. The pump chamber diameter is 13 mm and the diffuser/nozzle element neck dimensions are 0.3×0.3 mm. Simplified theoretical analyses of the maximum pump flow and resonance frequency are given. The flow rectifying ability of the diffuser/nozzle elements is demonstrated in a stationary flow situation and the pump performance is verified in two different pump mode configurations: anti-phase and in-phase chamber volume excitation. The measurements in the anti-phase mode show pump flows and pump pressures which are more than twice as high as those of the in-phase oscillation mode. The anti-phase mode has a pump capacity of about 16 ml/min and a maximum pump pressure of about 1.7 m H2O with the pump diaphragm vibration frequency set to the pump resonance frequency of 540 Hz.

Working principle and performance of the dynamic micropump

Abstract: This paper deals with a piezoelectrically driven micropump of the reciprocating type. For the flux rectification, so-called dynamic passive valves, particularly shaped micro channels having a direction-dependent fluid-dynamic behaviour, are used. This solution renders the pump structure extremely simple and makes the fabrication process cheap. Also, further miniaturization becomes possible. Typical working parameters are zero-load pump rates of several hundred microlitres per minute and pump pressures of up to 7 kPa. The upper frequency limit is as high as about 10 kHz. Thus, pumping of gases at resonance operation also becomes possible. A quasistatic model has been developed which enables an optimized application-oriented layout process to be carried out.

Surface micromachined microengine

Abstract: The design, fabrication, and preliminary testing of a polysilicon microengine are presented. In this early work, electrostatic comb-drive actuation is used to demonstrate the microengine. However, the basic gear/link element of the microengine can be driven by any suitably forceful linear actuators. This device has direct application as a drive and power source for micromachined mechanisms such as optical switches, electrical switches, micropositioners, or any other micro-sized device requiring mechanical power. This is the first device of its kind that is directly linked to an output gear and converts linear motion from comb-drive actuators to rotational motion. The microengine provides output in the form of a continuously rotating output gear (≈ 50 μm in diameter) that is capable of delivering torque to a micromechanism. The microengine can be operated at varying speeds and its motion can be reversed. Processing considerations address the elimination of natural interferences that arise when conformally deposited polysilicon films form the links, joints, and gears that comprise the microengine. The resultant device is completely batch fabricated without the need for piece-part assembly.

Selection of glass, anodic bonding conditions and material compatibility for silicon-glass capacitive sensors

Abstract: This paper examines the process of anodic bonding with regard to the fabrication of silicon-glass capacitive sensors. Various glasses are assessed in terms of the suitability of their physical properties and results are presented on flatness control of these glasses when bonded to silicon at different temperatures. Many of the problems which can typically affect silicon-glass sensors are examined and explained in terms of the anodic bonding process. Effects such as the electrolysis of the glass and the transport of the oxygen produced in this process are discussed and design considerations for minimising deleterious effects of this oxygen are presented. We demonstrate the process of selection of glass, bonding parameters and other material selection by reference to a device on which we are currently working.

Fabrication and characterization of PZT thin-film vibrators for micromotors

Abstract: For the first time we have characterized a micromotor driven by a piezoelectric PZT (PbZrxTi1-xO3) thin film. Sputter and sol-gel techniques have been applied for the deposition of the PZT films onto a silicon stator membrane, which is 20-30 mu m thick and has a diameter of 4 mm. The amplitudes of the membrane deflections are measured by means of laser interferometry. They are as large as 800 nm V-1 at the first resonance (26 kHz) and 60 nm V-1 at 1 kHz. This is one order of magnitude larger than previously reported for a ZnO-activated device of similar geometry. The motor operates at 1-3 V-r.m.s., with speeds of up to 200 rpm at 1.1 V-r.m.s. and torques of 35 nN m at 2.5 V-r.m.s. and 1 mN force between rotor and stator. Compared with the conceptually identical ZnO version published by Racine et al., this is an improvement by a factor of three in speed per volt. Taking into account the linear increase of the torque with the stator vibration frequency, the torque per volt is a factor of two higher. A long-term test of 100 h showed no degradation of the motor performance.

Surface acoustic wave atomizer

Abstract: An application of a surface acoustic wave device for miniaturization of ultrasonic atomizers and for functional system construction is proposed. Actually, ultrasonic atomizers are rather smaller than those produced by other methods, so that nebulizers that are handy to carry use ultrasonic vibration. However, they are too large for a pocket or a catheter. A fine mist has been obtained with the first trial of a surface acoustic wave atomizing device whose dimensions are pocket size. There is a possibility of this functional device being reduced to a system of millimetre size. The atomizer consists of a vibrator, a cover and a tube. The vibrator and cover material are 127.8° Y-cut LiNbO3 to generate a Rayleigh wave, a kind of surface acoustic wave. The Rayleigh wave is the driving force of the pumping and atomizing effects. The pumping effect is caused by the wave motion of the elastic material and viscosity of the fluid, like an ultrasonic motor. The atomizing rate varies according to the driving voltage. The maximum rate is about 0.6 ml min−1 at around 10 MHz. The linear mean diameter is 19 μm and the Sauter's mean diameter is 34 μm. A smaller device that operates at 47 MHz is also demonstrated.

Operational principle, fabrication and displacement characteristics of a functionally gradient piezoelectric ceramic actuator

Abstract: In this paper, the theoretical relationship between the bending displacement at the free end of a functionally gradient material (FGM) actuator and the FGM coefficient of the sandwich has been derived from the structure of an FGM actuator. FGM actuators based on PNN-PZT piezoelectric ceramics have been developed by the powder mould stacking press method and their displacement characteristics have also been measured. The results show that the bending displacement at the free end of a 20 mm×8 mm×0.7 mm FGM actuator is about 20 μm when a voltage of 1000 V is applied. The morphology and the compositional distribution across the profile of the FGM actuator are examined by using SEM and EDS, respectively.

Airbag application: a microsystem including a silicon capacitive accelerometer, CMOS switched capacitor electronics and true self-test capability

Abstract: A low cost, high reliability accelerometer microsystem designed for crash sensing in automotive airbag electronic control units is presented. The proposed microsystem offers high level output, on-line self-test function, small size (3.5 mm × 3.5 mm × 1.15 mm), and high design flexibility thanks to a two-chip construction. The sensitive part is a surface micromachined capacitive interdigitated structure realized from a SIMOX SOI substrate. The accelerometer operates in a closed loop mode using electrostatic feedback with conditioning circuitry realized in a 2 μm CMOS process. A high performance readout circuit using switched capacitors has been developed. Behavioural simulation results show a bandwidth of 630 Hz at ±50 g with 5 V power supply. The fabrication process includes the realization of a free-standing seismic mass by means of reactive ion etching and sacrificial oxide etching, the mechanical protection of the sensing element with a thin silicon cap bonded onto the structured SOI wafer, and eventually the electrical connection with the ASIC by flip-chip bonding. Preliminary results are very encouraging: dynamic actuation of the sensing elements is optically tested, with a yield of 70% at a prototype level. Excellent shock resistance and low internal stress are observed.

A micromachined vibrating gyroscope

Abstract: A vibrating microgyroscope with a thin polysilicon resonator fabricated by silicon surface micromachining is described. The 400 μm × 800 μm resonator is driven in a lateral direction by electrostatic force, and the angular rate is detected as the capacitance change between the resonator and its substrate. Mechanical Q -factors for the driving mode and the detecting mode of the polysilicon resonator are 2800 and 16 000, respectively, at pressures below 0.1 Pa. Methods are presented for modifying the difference between the resonance frequencies of the driving and detecting modes. The test device shows a noise-equivalent rate of 2° s −1 .

Micromachined free-space integrated micro-optics

Abstract: The surface-micromachining technique has been employed to fabricate novel three-dimensional micro-optical elements for free-space integrated optics. The optical axes of these optical elements are parallel to the substrate, which enables the entire free-space optical system to be integrated on a single substrate. Microscale Fresnel lenses, mirrors, beam splitters, gratings, and precision optical mounts have been successfully fabricated and characterized. In addition, micropositioners such as rotary stages and linear translational stages are monolithically integrated with the optical components using the same surface-micromachining process to provide on-chip optical alignment or optomechanical switching. Self-aligned hybrid integration with semiconductor edge-emitting lasers and vertical cavity surface-emitting lasers are also demonstrated for the first time. This new free-space micro-optical bench (FSMOB) technology could significantly reduce the size, weight, and cost of most optical systems, and could have a significant impact on optical switching, optical sensing and optical data-storage systems as well as on the packaging of optoelectronic components.

Application of conducting polymer technology in microsystems

Abstract: Conducting polymers are a new type of organic material that offer enormous potential for application within the field of microsystems. In this paper we review the basic properties of conducting polymers and discuss their application in electronic, mechanical and (bio)chemical microsystems. For instance, we have found that thin films of poly(pyrrole)/decanesulfonate have both a low friction coefficient (ca. 0.1) and wear rate (ca. 1 nm cm −1 ) that are similar to values observed for PTFE, yet possess relatively high electrical and thermal conductivities. In addition, conducting polymers can be readily electrodeposited onto planar or curved micromechanical structures, such as microslideways, micromotors or microturbines, to provide a bearing material of superior performance to standard micro-engineered materials (e.g. Si, SiO 2 , Si 3 N 4 ) and better processability than PTFE. In addition, conducting polymers can be used as gas-sensitive films in microelectronic devices. They have been shown to have a rapid, reversible ppm sensitivity to polar organic compounds (e.g. alcohols, ketones, aldehydes and fatty acids) without interference from common gases such as CO 2 , CO, CH 4 and N 2 . Conducting polymers are currently being used in commercial electronic noses, and integrated microsystems are being realised with the advent of custom microsensor array devices and application-specific integrated circuit chips.

SOI 'SIMOX'; from bulk to surface micromachining, a new age for silicon sensors and actuators

Abstract: Separation by ion implantation of oxygen (SIMOX), today an industrial 'silicon on insulator (SOI) substrate', allows a number of improvements for silicon sensors or actuators. For piezoresistive detection, the silicon top layer (0.2 μm thick) is used as an active material with the excellent properties of the single-crystalline silicon. Thanks to its very good electrical insulation from the substrate, high temperature sensors (up to 300 °C) with low noise and high dynamic range can be obtained. These devices are generally and preferably made by bulk micromachining for high performance sensors. Another important aspect of this substrate is its ability to get, by epitaxy, a high mechanical quality silicon layer (thickness > 10 μm) for surface micro-machining and the electronic circuits integration for smart sensors. Capacitive detection seems to be most suitable for miniaturised and cheaper surface microstructures. In the case of sensors (pressure or acceleration) with the detection axis perpendicular to the substrate, a higher capacitance variation is obtained due to the thinness of the SiO 2 sacrificial layer (0.4 μm). This high sensitivity allows a reduction of the sensor area. For acceleration sensors with the detection axis parallel to the substrate, the high thickness of the epitaxial silicon layer allows high stiffness ratio which reduces the sticking effect. Moreover, deep dry etching of silicon, which is today a mature technology, provides higher capacitance variation. The last but not the least advantage is the possibility, thanks to the low thickness of the superficial stack (0.6 μm for both layers), to get localised buried electrodes by deep implantation before the epitaxial process. With this extra electrode, the parasitic capacitance can be reduced and the characteristics of the sensor or the actuator improved.

Infrared thermopile sensors with high sensitivity and very low temperature coefficient

Abstract: Unlike the 'classical' thermoelectric materials bismuth and antimony, the sensor material silicon allows a good compatibility to CMOS-standard IC processes. This paper describes micromachined IR thermopiles based on polysilicon and aluminium for the contactless measurement of surface temperature. The sensor performance shows high detectivity and very small temperature dependence of responsivity.

A silicon force sensor for robotics and medicine

Abstract: This paper describes the development of a silicon-based force sensor packaged in a flexible polyimide-based package. The fabrication process is compatible with standard integrated circuit processes and produces a flexible package that sandwiches the metal leads between protective polyimide layers. Silicon direct bonding and bulk micromachining (both isotropic and anisotropic) are utilized to fabricate the silicon sensing element. The sensing element consists of a circular diaphragm (200 μm thick with a 200 μm radius) over a 10 μm deep sealed cavity. The shallow capacity depth provides built-in overforce protection. The diaphragm is instrumented with piezoresistors in a Wheatstone bridge configuration. Sensitivity to force is realized via the addition of a solid dome over the silicon diaphragm. The dome transmits the applied force to the diaphragm. Torlon and epoxy domes are bench tested. The epoxy dome produces significant hysteresis, while the Torlon dome shows low hysteresis (2.4% of the mean output) and low nonrepeatability ( −1 N −1 are typical. The response is linear for low forces (

Silicon anisotropic etching in KOH-isopropanol etchant

Abstract: Silicon monocrystalline wafers of (100), (110) and (111) orientations are etched in KOH-isopropanol solution. SiO 2 layers patterned with a few types of figures are used as a mask for the etching of holes or islands. The planes that disappear and develop during the etching process are pointed out. the shapes of the etched figures are compared with the crystallographic description of silicon structure.

Sealed-cavity resonant microbeam pressure sensor

Abstract: A quasi-digital pressure sensor based on polysilicon resonant microbeams has been demonstrated. Pressure sensitivities of nearly 4000 counts per second per psi have been attained on a 10 psi device with a base frequency of 233 000 Hz. Short-term stability as low as 0.01 ppm of the base frequency is typical. The microbeams are fabricated with their own integral vacuum cavities, allowing high-Q operation in the differential pressure mode or in contact with liquids such as silicone oil. Design considerations include the effects of internal strain and lead to a push-pull layout configuration independent of microbeam strain or diaphragm thickness. Fabrication technology incorporates fine-grained polysilicon, surface micromachining, bulk micromachining, and reactive sealing. Packaging into precision avionics headers is being used for preliminary testing. Testing results indicate suitability for precision avionics, industrial, and commercial applications. Optical methods have been used to test resonant microbeam pressure sensors and verify the push-pull design methodology. Testing methods developed under this effort include electrostatic drive/piezoresistive sensing, optical drive/optical sensing, substrate piezoelectric drive/optical sensing, and electrostatic drive/laser vibrometer sensing. Wafer-level testing of 200 μm×46 μm×1.9 μm microbeams shows an average fundamental frequency of 553 150 and first overtone of 1 332 550 Hz. The standard deviations across the wafer are 0.15 and 0.10%, respectively. The internal strain and effective thickness can be determined with high resolution. Laser vibrometer measurements through the microbeam shell verify the fundamental frequency and reveal at least ten overtones up to 25 MHz.

Dissipation measurements of vacuum-operated single-crystal silicon microresonators

Abstract: The quality factors of vacuum-operated single-crystal silicon microresonators have been measured, to identify their important sources of mechanical loss when medium-related loss is absent. The microresonators are torsional structures consisting of beams of width ≈ 0.7 μm, fabricated by reactive-ion etching from a single-crystal silicon substrate. For torsional microresonators having Q-factors around 50 000, doping-impurity and support-related losses do not seem to be significant. Rather, it appears that losses originating from beam surfaces, which are dry-etched, are important. This etched-surface loss can be halved by thermal oxidation, resulting in microresonators with Q-values consistently in the range 80 000–100 000. A model for this surface-related loss is presented.

An ultrasonic micromotor using a bending cylindrical transducer based on PZT thin film

Abstract: Ultrasonic motors have a good high-torque performance. In particular, it seems that cylinder-type ultrasonic motors are superior to disk- or ring-type ones in the sense of high-torque application. For miniaturization of the motor size, a simple structure of an ultrasonic transducer becomes effective. This paper presents an ultrasonic micromotor using a bending cylindrical transducer based on a lead zirconate titanate (PZT) thin film on the side wall of a small tube. The transducer of the ultrasonic motor consists of a short cylindrical titanium pipe, PZT thin film and electrodes. The titanium pipe is introduced as a base material on which to deposit the PZT thin film by a hydrothermal method. The thickness of the film is about 9 μm. The electrodes are divided into four parts in a circumferential direction to excite degenerate bending vibration modes with two r.f. driving electrical sources. A rotor loaded on the transducer turns in the intended direction. The maximum revolution speed is 295 rpm.

Compensation of hysteresis in solid-state actuators

Abstract: In order to control piezoelectric or magnetostrictive solid-state actuators in a hysteresis-free way, the electric or magnetic polarization in the active material must be controlled. The actuating signal is modified by an inverse system so as to show a hysteresis-free, linear transfer characteristic by the concatenation of the inverse system with the actuator. The hysteresis is described by a Preisach model. Measurements of magnetostrictive Terfenol-D demonstrate that almost complete compensation of the flux density/field strength characteristic curve can be obtained.

Microfabrication of complex surface topographies using grey-tone lithography

Abstract: This paper reports on a study of a methodology for fabrication of relief shaped microstructures using technologies common to standard IC manufacturing processes. Particular emphasis is put on the design and use of halftone transmission masks for the lithography step required in the fabrication process of mechanical, optical or electronic components. The design and experimental investigation of grey-tone masks is supported by lithography simulation. Results are presented for both, simulated grey-tone patterns as well as experimental profiles.

Fluid density sensor based on resonance vibration

Abstract: This paper presents the first silicon tube resonant fluid density sensor. The sensor is based on a tube system which is vibrated in a selected balanced mixed torsion and bending mode. The resonant frequency changes with the density of the fluid in the tube due to the change of the inertial mass of the vibrating tube system. A simplified analytical analysis shows that the resonance vibration frequency depends on the weighted density, ρ, as ∼ 1 ρ 1 2 , where ρ is the density of the silicon and the fluid weighted in accordance to their area in a cross section of the tube. The sensor was fabricated using double-sided silicon KOH etching and silicon fusion bonding. The silicon tube system (without the frame) is 8.6×17.7 mm with a thickness of 1 mm. The tube system was excited electrostatically into resonance vibration which was detected optically. The resonant frequency was measured for different mixtures of 2-propanol and water. The sensor shows very good sensitivity, −200 ppm (kg m −3 ) −1 and a high mechanical Q -value, of the order of 1500. The sample volume is only 0.035 ml.

Silicon accelerometer based on thermopiles

Abstract: Today, silicon sensors are becoming increasingly interesting for applications in the consumer industries, such as in washing machines, air conditioners, cars, home security systems and domestic scales. The market for accelerometers is first in the automotive industry, for airbags or ABS; but applications in TV or computer systems are also a possibility. For such applications, small and low-cost sensors will be needed in large numbers, which is why silicon sensors will be more advantageous than conventional sensors. This paper describes the second, much improved, design of an accelerometer incorporating thermopiles. This new type of accelerometer is relatively insensitive to temperature changes, mounting stress and interferences from electromagnetic fields. The sensor might be suited to work even under the hostile conditions that occur in automobiles.

Photolithography on micromachined 3D surfaces using electrodeposited photoresists

Abstract: Photolithography on micromachined 3D surfaces is becoming a key process for the fabrication of a wide range of novel micromechanical devices. Due to the surface tension, photoresists deposited as a liquid cause problems at sharp corners, which occur commonly in micromachined silicon devices. This paper describes the application of an electrodepositable ultraviolet sensitive photoresist, which is commercially available and which is already used in printed circuit board production. Process considerations are discussed to apply this technology successfully to silicon substrates. The results show the feasibility of photolithography on surfaces with anisotropically etched 200 μm deep cavities in (100) silicon.

Fabrication and characterization of high g-force, silicon piezoresistive accelerometers

Abstract: A high g-force, cantilever beam type accelerometer has been fabricated using silicon micromachining and diffusion techniques. The fabricated devices have been subjected to static and shock tests up to 10 000g. High g-force tests up to 100 000g were also performed on a selected number of devices using a Hopkinson's bar. The design modeling procedures and results are reported and the fabrication steps are described. Experimental results on sensitivity, linearity and resonance frequency are presented and compared with the theoretical values. The temperature dependence of the sensitivity is also determined and is described in detail. The devices are capable of performing up to 100 000g, have an average measured sensitivity of 0.72 μV g−1 with a 5 V bridge excitation voltage, and resonance frequencies greater than 100 kHz.

Magnetic sensors continue to advance towards perfection

Abstract: This work gives an up-to-date review of the new trends of solid-state magnetosensors such as orthogonal and parallel-field Hall devices, bipolar magnetotransistors (BMTs) and related transducers, multisensors for magnetic field, temperature and light, vector and gradient magnetometers, etc. Intense research aimed at the implementation of biomagnetosensors has been proposed.

Large-area 1D thin-film position-sensitive detector with high detection resolution

Abstract: The aim of this work is to present the main optoelectronic characteristics of large-area one-dimensional position-sensitive detectors (1D TFPSDs) based on amorphous silicon (a-Si) p-i-n diodes. From that, the device resolution, response time and detectivity (defined as being the reciprocal of the noise equivalent power pattern) are derived and discussed concerning the field of applications of the 1D TFPSDs.