IRST ANALYSIS REPORT

Transcription

1 IRST ANALYSIS REPORT Report Prepared by: Everett George Dahlgren Division Naval Surface Warfare Center Electro-Optical Systems Branch (F44) Dahlgren, VA Technical Revision: Format Revision: / 12

2 TABLE OF CONTENTS 1.0 INTRODUCTION TARGET TYPES AND TEST CONDITIONS SOURCE OF TARGET SIGNATURES TARGET SNR AT HORIZON OBSCURATION SUMMARY REFERENCES ABBREVIATIONS...5 A.0 DETERMINATION OF TARGET INITIAL DETECTION...6 A.1 DEFINITION OF TARGET INITIAL DETECTION...6 A.2 ESTIMATION OF TARGET BANDWIDTH INTENSITY...8 A.3 WEATHER CONDITIONS CONSIDERED...8 B.0 DETERMINATION OF HORIZON BLOCKAGE RANGE...9 B.1 EQUATION DERIVATION...9 B.2 DERIVATION ASSUMPTIONS...10 C.0 DERIVATION OF ELEVATION ANGLE RELATIVE TO SENSOR...11 C.1 ELEVATION DERIVATION...11 C.2 DERIVATION ASSUMPTIONS / 12

3 1.0 INTRODUCTION The objective of this report is to summarize results of performance analyses conducted for an infrared search & track (IRST) sensor. The analyses predict IRST initial detection ranges of targets radially inbound at constant speed and altitude under test conditions. The Random 400 (R400) World-Wide Environment data set is used to statistically model atmospheric characteristics. Initial detection ranges, considered here, are the ranges at which target contrast irradiance is equal to a specific sensor noise-equivalent-irradiance (NEI) multiplied by a set threshold-to-noise ratio (TNR). These ranges do not take into account sensor rotation or lag time. Target contrast irradiance is calculated considering the target as a point source with radiation having atmospheric attenuation described by a propagation range, extinction coefficient, and range correction factor. In the contrast irradiance, it is further assumed that foreground and background irradiances are equivalent in magnitude and cancel out contrast irradiance contributions. Appendix A, Appendix B, and Appendix C describe further assumptions and equations used in this report. For each of the analysis conditions, initial detection ranges are calculated in the R400 data set for sensor with a NEI Watts per square-centimeter. 2.0 TARGET TYPES AND TEST CONDITIONS Table I shows target types and other Sensor Target -- Target Intensity -- Target Altitude μm parameters used to describe (#) (ft) (ft) (W/str) (W/str) anticipated test conditions for the IRST. Column (1) of Table I identifies BLANKED the target type. Columns (2) and (3) of Table I indicate the sensor height (assumed meters) and target heights, respectively, above sea level. Columns (4) and (5) list bandwidth average target intensities for micron micron bandwidths, respectively. Target intensity values are based on data specified in Table II. Derivation of target intensities is described in Appendix A. 3.0 SOURCE OF TARGET SIGNATURES Table II identifies the target signature data used in determining the target intensities for the analysis. Signatures are chosen which most closely match the test conditions for the IRST. Column (1) of Table II identifies the target type. Column (2) of Table II Table I Assumed Target Conditions at IRST Test (1) (2) (3) (4) (5) Table II Target Signature Data & Description (1) (2) (3) (4) (5) (6) (7) Target Signature Speed Altitude Train Elev Aspect (#) File (Mach) (km) (deg) (deg) (-) BLANKED indicates the FTD format signature file which provided spectral intensity data of each target. Columns (3) through (7) reflect the conditions at which the spectral signature data was taken or calculated. This data is cited directly from the FTD format signature file. Column (3) identifies target speed. Column (4) identifies target altitude. Columns (5) and (6) give the aspect train and elevation angles, respectively, of the target. Column (7) gives the assigned aspect number of the target orientation. 3 / 12

4 4.0 TARGET SNR AT HORIZON OBSCURATION Table III and Table IV indicate signalto-noise (SNR) ratios which are present at the sensor from targets at horizon obscuration. This data is provided to indicate under what circumstances detection of the targets would be horizon limited. The SNRs consider target irradiance with attenuation in the best conditions of the R400 data set and irradiance with no atmospheric attenuation. Column (1) identifies the target type. Column (2) gives the target intensity as stated in Table I. Column (3) lists the target range at which horizon blockage occurs (horizon blockage range (HBR)). Column (4) lists the SNR of the target which would occur at HBR if no atmospheric attenuation were present (transmission is unity, i.e., in a vacuum). Column (5) indicates the highest occurrences of R400 transmission at HBR in the bandwidths under consideration. Column (6) gives the best SNR obtainable in the R400 data set for the target at HBR. Values in column (6) are the product of values in column (4) and column (5). In micron bandwidth, the clearest R400 day has an extinction coefficient (1 / km) with a range correction factor In micron bandwidth, the clearest R400 day is recorded with an extinction coefficient (1 / km) and a range correction factor Determination of HBR is described in Appendix B. 5.0 SUMMARY Using the R400 World-Wide Environment data set, variations in initial detection ranges have been established for several test targets. When an IR sensor with NEI Watts per square-centimeter is considered with all test targets are detected within HBR in all R400 conditions for both of the IR bandwidths considered. Table III Target SNR at Horizon Blockage micron Bandwidth (1) (2) (3) (4) (5) (6) Clearest Target Blockage Vacuum -- R Target Intensity Range SNR Trans SNR (#) (W/str) (nm) (-) (-) (-) BLANKED Table IV Target SNR at Horizon Blockage micron Bandwidth (1) (2) (3) (4) (5) (6) Clearest Target Blockage Trans=1 -- R Target Intensity Range SNR Trans SNR (#) (W/str) (nm) (-) (-) (-) BLANKED Table Percentile Target Detection Ranges micron IR Bandwidth Targets: T-1 T-2 T-3 T-4 T-5 T-6 Prob TNR Initial Detection Range (%) (-) (nautical miles) BLANKED Table V and Table VI give initial detection distances of targets for percentile cases. Detection distances are expressed in nautical miles and given for sensor Each distance indicates that, percent of the time, weather conditions will permit detection of the target within the stated value. Table V and Table VI show that the targets consistently have greater detection distances in micron band than in micron band. Because of their similarity in signatures, targets T-2, T-3, and T-4 have approximately the same initial detection distances. In addition, targets T-2, T-3, and T-4 have the largest 4 / 12

5 detection distances of all the targets considered. In the to micron band, targets T-1 and T-6 have roughly the same intensities due to similarity in localized spectral intensities. However, target T-1 has greater detection distances in the to micron band due to higher localized spectral intensities. Because of its small signature intensity, target T-5 consistently has the smallest detection ranges in all categories. Table VI & Percentile Target Detection Ranges in to Micron IR Bandwidth Targets: T-1 T-2 T-3 T-4 T-5 T-6 Prob TNR Initial Detection Range (%) (-) (nautical miles) BLANKED 6.0 REFERENCES [1] Rudzinsky, Marilyn R., "Contrast Irradiance Verses Range Program" (CONTIRR Version 6.1), NSWC Dahlgren Division Internal Program Source Code, Dahlgren, Virginia, 30 October [2] Hepfer, Kenneth C., "Simple TIS / TVS Range Model", NSWC Dahlgren Division Internal Report, Dahlgren, Virgnia, 17 January [3] Harvey, R.N., et al, "AN / SAR-8 Air Target Performance: Analysis Methodology and Threat Predictions", NSWC TR , NSWC Dahlgren Division, Dahlgren, Virginia, September [4] Hepfer, Kenneth C., "BAND_AV4 Program Version 4", NSWC Dahlgren Division Internal Source Code and Output, Dahlgren, Virginia, 13 November [5] Bronshtein, I.N., et al, Handbook of Mathematics, 1st Edition, Van Nostrand Reinhold Company, New York, New York, ABBREVIATIONS The following list identifies abbreviations used in the tables and text of this report and the appendices: deg - degree Elev - elevation ft - feet HBR - horizon blockage range IRST - infrared search & track km - kilometer NEI - noise-equivalent-irradiance nm - nautical mile Prob - probability R400 - Random 400 SNR - signal-to-noise ratio str - steradian TNR - threshold-to-noise ratio Trans - transmission μm - micron W - Watt 5 / 12

6 A.0 DETERMINATION OF TARGET INITIAL DETECTION This appendix describes equations and definitions used to estimate infrared search & track (IRST) sensor initial detection of a point source target. The formulas derived here are primarily used to determine if sensor detection of a target is limited by horizon blockage or target intensity. A.1 DEFINITION OF TARGET INITIAL DETECTION Based on information in Reference [1], target contrast irradiance for a specific sensor bandwidth can be estimated as: μ 2 C i = K μ 1 τ J e A t N f N b R 2 dμ (A-1) C i - bandwidth contrast irradiance (W / cm 2 ) K - conversion constant (1.0E-10 km 2 / cm 2 ) τ - spectral atmospheric transmission R - target range from sensor (km) A t - target projected area (cm 2 ) J e - spectral target intensity (W / str / cm -1 ) N f - spectral atmospheric foreground radiance (W / cm 2 / str / cm -1 ) N b - spectral atmospheric background radiance (W / cm 2 / str / cm -1 ) μ 1 - wavenumber of lower bandwidth bound (cm -1 ) μ 2 - wavenumber of upper bandwidth bound (cm -1 ) μ - wavenumber variable of integration (cm -1 ) Considering that detection of the target will occur near HBR, it is assumed that atmospheric foreground radiance contributions will be approximate to background radiance and that the atmospheric radiance terms will cancel. Equation A-1 then simplifies to: μ 2 C i = K μ 1 τ J e dμ (A-2) 2 R To simplify calculations, it is further assumed that the target range is constant with respect to the integral, and that the bandwidth integral of the product transmission times intensity can be approximated by the product of the bandwidth integrals transmission and intensity. Here, target intensity is set independent of atmospheric conditions. Equation A-2 is simplified to: μ 2 μ 2 J e dμ C i = K τ dμ R 2 μ 1 μ 1 Bandwidth average transmission and target intensity are defined as follows: (A-3) μ 2 τ b = τ dμ μ 1 (A-4) 6 / 12

7 μ 2 J eb = J e dμ μ 1 (A-5) τ b J eb - bandwidth average atmospheric transmission - bandwidth average target intensity (W / str) With Equation A-4 and Equation A-5 substituted into Equation A-3, contrast irradiance can be estimated through the following equation: C i = K τ b J eb R 2 (A-6) Per Reference [2], bandwidth average atmospheric transmission (used in Equation A-6) can be evaluated from the following equation: τ b = e α R 10 x R n (A-7) α x n - atmospheric extinction coefficient (1 / km) - range correction factor In Equation A-7, the atmospheric extinction coefficient is determined at 10 kilometers. The x n term applies a correction such that transmission is also a perfect fit at 20 kilometers. Sensor detection of a target is assumed when target contrast irradiance is at or above a given threshold set for the sensor. Per Reference [1], initial detection of the target is assumed to occur when target contrast irradiance equals the sensor threshold as described in the following equation: C i = TNR NEI (A-8) TNR - threshold to noise ratio NEI - noise equivalent irradiance (W / cm 2 ) Combining Equation A-6, Equation A-7, and Equation A-8: TNR NEI = K J eb R 10 x R 2 e α R r (A-9) By iteratively changing target range, Equation A-9 can be evaluated to estimate target range at initial detection. 7 / 12

8 A.2 ESTIMATION OF TARGET BANDWIDTH INTENSITY FTD format spectral signatures of targets are used to estimate target intensities in the and micron IR bands. The signatures express intensity of the target as a function of wavelength. To determine the bandwidth intensity of the target, Equation A-5 can be approximated with the signature data using the trapezoid integration approximation. This approximation is expressed in the following equation: n J eb 1 2 [J e μ i 1 J e μ i ] μ i 1 μ i (A-10) i=1 μ i - spectral wavenumber at which to evaluate target spectral intensity (cm -1 ) J e(μ i) - target spectral intensity at wavenumber μ i (W / str / cm -1 ) n - number of data points at which spectral intensity is evaluated A.3 WEATHER CONDITIONS CONSIDERED The Random 400 (R400) World-Wide Environment Data Set (Reference [3]) is used to describe weather conditions for the IRST application. The data set contains 400 measurement samples which statistically describe weather in which Navy shipboard sensors are expected to operate. The data is collected from several different locations and under many conditions. Figure A-1 shows global locations from which the meteorological data was taken. The locations are considered representative weather. Figure A-1 Global Locations Used for R400 Data Measurements For this analysis, weather conditions are described through Equation A-7. From transmittance output of Reference [4], data files supply bandwidth average atmospheric extinction coefficients and range correction factors for each of the 400 data samples in conjunction with micron infrared bands. 8 / 12

9 B.0 DETERMINATION OF HORIZON BLOCKAGE RANGE This appendix derives the formula used to estimate horizon blockage range (HBR) of a target with respect to an infrared (IR) sensor in a maritime environment. With both the sensor and target at fixed altitudes above sea level, HBR is the furthermost target distance from the sensor at which light emitted from the target is not blocked by the earth's surface. The target image is obscured by the horizon at distances greater than HBR. Horizon blockage of the target image does not occur at distances less than HBR. For this derivation, the following parameters determine HBR: h s h t r e f r - sensor height above sea level - target height above sea level - earth radius - refraction factor B.1 EQUATION DERIVATION Refractive bending of light rays which travel near the earth's surface can be estimated by assuming an earth radius modified from the actual value. Change in radius is specified through a refraction factor in the following equation: r f = f r r e (B-1) r f - apparent refractive earth radius (km) The refraction factor is dependent on radiation wavelength, propagation distance, and atmospheric / oceanic conditions. To derive HBR through trigonometric analysis, right triangles are formed between the sensor location, horizon, and earth's center, and between the target location, horizon, and earth's center (see Figure B-1). Using the Pythagorean theorem (Reference [5]), HBR can be expressed through the following equation assuming a spherical earth: Figure B- 1 Geometric Representation of HBR HBR = h s r f 2 r f 2 h t r f 2 r f 2 (B-2) Expanding the squared sums and canceling like terms of Equation B-2: HBR = h s 2 2r f h s h t 2 2 r f h t (B-3) When target and sensor heights are considered near the earth's surface, the earth's radius is much greater in magnitude than the values of the heights. Provided the refractive factor has a magnitude near one or greater, the following simplifications can be made: h s 2 2 r f h s 2 r f h s for r f h s (B-4) 9 / 12

10 h t 2 2r f h t 2r f h t for r f h t (B-5) Substituting Equation B-4 and Equation B-5 into Equation B-3 and grouping like terms: HBR 2 r f h s h t (B-6) Substituting Equation B-1 into Equation B-6: HBR 2 f r r e h s h t (B-7) With the refraction factor set at seven-sixths for infrared radiation, the earth radius taken at approximately 6360 kilometers, target and sensor heights expressed in meters, and HBR expressed in kilometers: 1 2 f r r e = [ 2 7 1km 6360km m ] km m Substituting Equation B-8 into Equation B-7: (B-8) HBR 3.85 h s h t (B-9) HBR h s h t - horizon blockage range (kilometers) - sensor height above sea level (meters) - target altitude above sea level (meters) B.2 DERIVATION ASSUMPTIONS Equation B-9 is based on the following assumptions: 1) The earth has a smooth spherical surface at constant radius. Wave action and variations from the assumed earth radius are not taken into account. 2) Refractive effects of target infrared radiation are approximated by a seven-sixths refractive factor. Refraction is dependent on weather conditions, spectral wavelength of radiation being considered, and radiation propagation path. 3) The target is a point source of infrared radiation. HBR of targets with large IR images would be dependent on target orientation, position, and configuration. 4) Target and sensor heights are relatively small when compared with the apparent refractive earth radius. 10 / 12

11 C.0 DERIVATION OF ELEVATION ANGLE RELATIVE TO SENSOR This appendix derives the formula used to estimate elevation angle of a target relative to an infrared (IR) sensor in a maritime environment. The elevation angle is measured in a vertical plane from the sensor horizontal with a sign convention of positive upward. The elevation angle is the perceived angle in the vertical plane at which the sensor would detect the target at a given range. For this derivation, the following parameters are used to express the elevation angle. h s h t r t r e f r - sensor height above sea level - target height above sea level - target range - earth radius - refraction factor C.1 ELEVATION DERIVATION Refractive bending of light rays which travel near the earth's surface can be estimated by assuming an earth radius modified from the actual value. Change in radius is specified through a refraction factor in the following equation: r f = f r r e (C-1) r f - apparent refractive earth radius (km) The refraction factor is dependent on radiation wavelength, propagation distance, and atmospheric / oceanic conditions. For IR radiation, the refractive factor is usually set to seven-sixths. To derive target elevation angle through a trigonometric analysis, a triangle is formed between the sensor location, target location and earth center (see Figure C-1). Assuming a spherical earth and using the Law of Cosines (Reference [5]), the angle at the sensor apex of the triangle (α) can be expressed through the following equation: Figure C-1 Geometric Representation of Target Elevation Angle h t r f 2 = r t 2 h s r f 2 2r t h s r f cos α (C-2) α - sensor apex angle (radians) Solving Equation C-2 for the sensor apex angle: 11 / 12

12 cos α = r 2 t r f h s 2 r f h t 2 2 r t r f h s (C-3) In Figure C-1, α and θ form a right angle. Then, considering the sign convention of the elevation angle, the sensor apex angle (α) of the target is given by the following equation in relation to the target elevation angle (θ): α = θ π 2 (C-4) θ - target elevation angle (radians) It follows from Equation C-4 and addition formulas of trigonometric functions (Reference [5]) that the cosine of the sensor apex angle (α) is equal to minus the sine of the elevation angle (θ): cos α = sin θ (C-5) Substituting Equation C-5 into Equation C-3 and solving for the target elevation angle (θ): [ θ = Asin r f h t 2 r f h s 2 2 r t ] (C-6) 2r t r f h s For sensors in which the reference zero elevation angle (θ) is at the horizon instead of the horizontal, the depression angle of the sensor from the horizontal to the horizon is subtracted from the target elevation angle (θ). C.2 DERIVATION ASSUMPTIONS Equation C-6 is based on the following assumptions: 1) Sensor and target heights are measured from the surface of a spherical earth with constant radius. Variations from the assumed earth radius are not taken into account. 2) Refractive effects of target infrared radiation are approximated by a seven-sixths refractive factor. Refraction is dependent on weather conditions, spectral wavelength of radiation being considered, and radiation propagation path. 3) The target is a point source of infrared radiation. Elevation angle of targets with large IR images would be variable. 12 / 12