1 6th Aquarius/SAC-D Science Meeting 19-21 July 2010 Seattle, Washington, USA NIRST L1 Algorithms Felipe Madero & Héctor Raimondo

2 6th Aquarius/SAC-D Science Meeting Seattle. Nirst Algs. F.Madero, H.Raimondo 2 of 34 July 19-21, 2010 NIRST Overview & characteristics

3 6th Aquarius/SAC-D Science Meeting Seattle. Nirst Algs. F.Madero, H.Raimondo 3 of 34 July 19-21, 2010 Overview & characteristics co-registration 11.8  m 10.8  m 3.8  m 1 2 3 1 2 3 MWIRLWIR Optical Axes Active lines : Band 1: LWIR2 Band 2: LWIR3 Band 3: MWIR2 Pixel 1 Pixel 512

4 6th Aquarius/SAC-D Science Meeting Seattle. Nirst Algs. F.Madero, H.Raimondo 4 of 34 July 19-21, 2010 Overview & characteristics

5 6th Aquarius/SAC-D Science Meeting Seattle. Nirst Algs. F.Madero, H.Raimondo 5 of 34 July 19-21, 2010 Products definitions & Processing levels Products definitions & Processing levels

6 6th Aquarius/SAC-D Science Meeting Seattle. Nirst Algs. F.Madero, H.Raimondo 6 of 34 July 19-21, 2010 Products definitions  Basic Products: Specification of the Processing Levels: Level 0A (raw counts) Level 1A (L0A + rel. rad. corr. + interband reg. + earth location) Level 1B1 (L1A + abs. rad. corr.) Level 1B2 (L0A + rel./abs. rad. corr. + map projection)  Derived Products: Fire Mapping & Fire Radiative Power Volcanic Activity Monitoring Sea Surface Temperature (SST) Land Surface Temperature (LST)

7 6th Aquarius/SAC-D Science Meeting Seattle. Nirst Algs. F.Madero, H.Raimondo 7 of 34 July 19-21, 2010 Basic Products – L0A Raw Sample Counts of the instrument. Without radiometric/geometric corrections. Easy to access: The User doesn't need to know the downlink format in order to work with the data. Includes telemetry from the spacecraft (eph, att) and from the sensor (timestamp, temperatures, etc). Includes all auxiliary information needed to make corrections: radiometric coefficients, geometric vectors and matrices, etc. Includes information related to the quality of the data (lost lines, crc problems, etc).

8 6th Aquarius/SAC-D Science Meeting Seattle. Nirst Algs. F.Madero, H.Raimondo 8 of 34 July 19-21, 2010 Basic Products – L1A Results from applying the following processes to the L0A data: Relative radiometric correction Inter-band registration Earth Location parameters calculation (included in the geoloc file) It doesn't contain absolute radiometric corrections (units are digital numbers). It doesn't contain any geometric corrections besides the inter-band registration. Contains telemetry information from the spacecraft and sensor. Contains information related to the quality of the data. Contains all the information needed for the remainder corrections (absolute radiometric correction coefficients, etc).

9 6th Aquarius/SAC-D Science Meeting Seattle. Nirst Algs. F.Madero, H.Raimondo 9 of 34 July 19-21, 2010 Geoloc File Contents A grid over the data is defined. Each point in the grid will contain:  Latitude  Longitude  Zenith angle to the spacecraft  Azimuth angle to the spacecraft  Range to the spacecraft  Zenith angle to the sun  Azimuth angle to the sun  Zenith angle to the moon  Azimuth angle to the moon

10 6th Aquarius/SAC-D Science Meeting Seattle. Nirst Algs. F.Madero, H.Raimondo 10 of 34 July 19-21, 2010 Basic Products – L1B - L1B1 Results from applying the following processes to the L1A data: Absolute radiometric correction. It doesn't contain any geometric corrections besides the inter-band registration. Contains telemetry information from the spacecraft and sensor. Contains information related to the quality of the data. Contains Earth Location Parameters (geoloc). Contains all the information needed for the remainder corrections It is the main product from which the derived products are generated

11 6th Aquarius/SAC-D Science Meeting Seattle. Nirst Algs. F.Madero, H.Raimondo 11 of 34 July 19-21, 2010 Basic Products – L1B - L1B2 Results from applying the following processes to the L0A data: Relative radiometric correction Absolute radiometric correction Resampling to a Map Projection Earth Location Parameters Calculation Contains information related to the quality of the data. Inter-band registration is obtained by resampling to the same output coordinates. Contains Earth Location Parameters (geoloc). Contains all the information needed for the remainder corrections

12 6th Aquarius/SAC-D Science Meeting Seattle. Nirst Algs. F.Madero, H.Raimondo 12 of 34 July 19-21, 2010 Characteristics

13 6th Aquarius/SAC-D Science Meeting Seattle. Nirst Algs. F.Madero, H.Raimondo 13 of 34 July 19-21, 2010 Processor: Project, Architecture and Flow Diagram Processor: Project, Architecture and Flow Diagram

14 6th Aquarius/SAC-D Science Meeting Seattle. Nirst Algs. F.Madero, H.Raimondo 14 of 34 July 19-21, 2010 The Nirst processor is being developed as part of the VNIP (Visible and Near Infrared Processors) project at CONAE. The VNIP System is defined as a set of units which shall be part of CUSS (Conae User Segment Service). The development is guided by a software prototype developed with Python. The testing will be supported by a NIRST simulator which is currently being developed, also using Python. The specification of the algorithms to the software provider is based on radiometric and ATBD documents, which were developed hand-in-hand with the software prototype. The design enables data based parallelization. Software Project

15 6th Aquarius/SAC-D Science Meeting Seattle. Nirst Algs. F.Madero, H.Raimondo 15 of 34 July 19-21, 2010 Execution Flow - NIRST

16 6th Aquarius/SAC-D Science Meeting Seattle. Nirst Algs. F.Madero, H.Raimondo 16 of 34 July 19-21, 2010 Science and Supplementary Data

17 6th Aquarius/SAC-D Science Meeting Seattle. Nirst Algs. F.Madero, H.Raimondo 17 of 34 July 19-21, 2010 Frame of NIRST (HKE - Supplementary data ) 512 pix * 3 ch * 2 By= 3072 Bytes 3072 + 64 +2 = 3138 Bytes Voltages, currents and temperatues (48 bytes) 32 positions * 2 Bytes = 64 Bytes Configuration, operating modes and instrument status (16 bytes) The HK frame is composed of 64 bytes. The first 48 (positions 0 to 23) are dedicated to data from the sensors of: temperatures (8 positions), voltages (8 positions) and currents (8 positions). The remainder 16 bytes (positions 24 to 31) are dedicated to configuration and operating mode of the instrument.

18 6th Aquarius/SAC-D Science Meeting Seattle. Nirst Algs. F.Madero, H.Raimondo 18 of 34 July 19-21, 2010 Supplementary Data - HKE The instrument HK contains the supplementary data, used by the processor in order to generate the L1 product. It is composed of:  Temperatures of the optics: NIRST operating temperature will be maintained between 10 and 18 ºC. If the optic's temperature go beyond this range, the 10.85 µm and 11.85 µm chanels will start to blur. Besides that, the radiometric correction coefficients may have a dependency on temperature.  Operating mode: Digital Test Mode Acquisition, Analog Test Mode Acquisition, and Observation Mode Acquisition.  Integration Percent: 25%, 50%, 75% and 100%, over the time of a line.  Mirror position: ±15 dgr respect the nadiral position (±30 dgr over earth).  Lines of µbolometers selected: informs on which of the 6 sensor arrays have been selected for the acquisition.

19 6th Aquarius/SAC-D Science Meeting Seattle. Nirst Algs. F.Madero, H.Raimondo 19 of 34 July 19-21, 2010 Science Data  The data provided by the optical head is digitalized using 15 bits, from which one bit is devoted to the sign. This data is stored in a memory of 16 bits, in order to a posteriori transfer it to the PAD computer. As a result, the most significant bit (MSB=bit 15), is filled with the dafult value ’0’.  The data does not directly represent a digital number (DN). It is coded with the recursive equation 1.6, so in order to obtain the DN a decoding is necesary, for each pixel, to use a look up table (LUT) provided by INO.

20 6th Aquarius/SAC-D Science Meeting Seattle. Nirst Algs. F.Madero, H.Raimondo 20 of 34 July 19-21, 2010 Radiometric Calibration

21 6th Aquarius/SAC-D Science Meeting Seattle. Nirst Algs. F.Madero, H.Raimondo 21 of 34 July 19-21, 2010 Goals  The objective is to measure the energy at top of atmosphere (TOA), generated by an extended source.  This energy can be expressed in L S (radiance) [W/m 2.sr] or in T B (brightness temperature) [Kº] (TOA).  The digital numbers (DN) measured by the sensor must be converted to T B : calibration Planck DN==> Ls==> T B orDN==> T B  The conversion from L S to T B is made by using the Planck equation.

22 6th Aquarius/SAC-D Science Meeting Seattle. Nirst Algs. F.Madero, H.Raimondo 22 of 34 July 19-21, 2010 Steps in NIRST calibration DN is an almost linear response of voltage across µbolometer. It is affected by an offset and a gain that are fixed in the electronics but are slightly different from pixel to pixel. Voltage across µbolometer is an almost linear result of its temperature change which is proportional to incident power. The whole process receives the name of responsivity and is a characteristic of each pixel. Φ(T) = Ω A ʃ L(λ,T) Ψ(λ) dλ Ω: Solid angle subtended by optics seen from the detector. A : Detector area (39 µm 2 ) Ψ : filters + optics L(λ,T) [ W/(m 2.sr.µm)]: TOA’s Spectral Radiance. (Planck´s law) Φ(T) [W] Power Radiance that reaches the µbolometer. TOA: Top Of Atmosphere

23 6th Aquarius/SAC-D Science Meeting Seattle. Nirst Algs. F.Madero, H.Raimondo 23 of 34 July 19-21, 2010 LUT The radiance Ls sensed at a particular chanel, originated from a black body with temperature T, is the weighted mean of the Planck function over the spectral response function of the channel (spectral function of the channel's filter): For each temperature T, The equation L S (T) will be numerically evaluated with: Tb  Ls LUT (look-up tables) realte the black body temperature with the sensor radiance. L S (T) = Σ L BB (λ,T).Ψ(λ).Δλ

24 6th Aquarius/SAC-D Science Meeting Seattle. Nirst Algs. F.Madero, H.Raimondo 24 of 34 July 19-21, 2010 Power (Φ) at the detectors Ada: area of the aperture diaphragm Dda: diameter of the aperture diaphragm Focal Length: f = 73mm F number: N = f/# = f/Dda = 1  f = Dda Area of the aperture diaphragm: Ada = π * (Dda/2) 2 = (π / 4) * f 2 Φ θ = Ls* Ada θ┴ * Ωd θ Φ 0 = Ls* (π / 4) * f 2 * Ad / f 2 Φ 0 = Ls * (π / 4) * Ad Φ θ = Ls * (π / 4) * f 2 *cos θ * (Ad / f 2 ). cos 3 θ Φ θ = Φ 0 * cos 4 θ Si: θ = 15.32/2  Φ θ = Φ 0 * 0.9646 Φ θ = Ls * (π / 4) * Ad * cos 4 θ (1)

25 6th Aquarius/SAC-D Science Meeting Seattle. Nirst Algs. F.Madero, H.Raimondo 25 of 34 July 19-21, 2010 Pre Lauch Calibration T BB [K]L S [W/(m 2.sr)]Ω[sr]Ad [m 2 ]Φd [W]DN P1…DN P512 300… …………………… 600… Green is measured at laboratory, red is calculated, black is data. Pre Lauch Radiometric Table At the laboratory, a gray body is used as the reference for a controlled and know temperature, and for each step of temperature (T BB ) digital number (DN) are obtained, for each pixel of each array. Using the LUT (Tb  Ls) radiances (Ls) associated to each brighness temperature T BB are obtained. Using the flux transfer equation Φd(θ) = Ls * (π / 4) * Ad * cos 4 θ (previous slide) a transformation from Ls to Φd (power at each detector) is made. Power Calibration Brightness Temperature Calibration

26 6th Aquarius/SAC-D Science Meeting Seattle. Nirst Algs. F.Madero, H.Raimondo 26 of 34 July 19-21, 2010 Relative and Absolute Calibration Φ vs. DN Φr = a0 r + a1 r *DN + a2 r *DN 2 + a3 r *DN 3 + … Absolute calibration: Φi =a0 r +a1 r *DNi RC +a2 r *(DNi RC ) 2 +a3 r *(DNi RC ) 3 +… DATE OF VALIDITY: Date from: Date until: RELATIVE CAL: 512 detectors x 6 line-microbolometer b0 i, b1 i, b2 i, b3 i … ABSOLUTE CAL: 1 x 6 line-microb a0 r, a1 r, a2 r, a3 r … TEMPERATURE RANGE: Date from: Date until: INTEGRATION %: (25%, 50%, 75% or 100%)

27 6th Aquarius/SAC-D Science Meeting Seattle. Nirst Algs. F.Madero, H.Raimondo 27 of 34 July 19-21, 2010 Pre–launch Radiometric Table: Li = a0r + b0r*DNi RC Lr = a0r + b0r*DNr Relative calibration: Absolute calibration: L S [W/(m 2.sr)]DN P1 DN P2 …DN P2048 047…5 Near saturt10191015…1022 DNi RC = b0i + b1i*Dni

28 6th Aquarius/SAC-D Science Meeting Seattle. Nirst Algs. F.Madero, H.Raimondo 28 of 34 July 19-21, 2010 Image in Brightness Temp. (DN  Tb) Calibration in Power Radiance Calibration in brightness temperature

29 6th Aquarius/SAC-D Science Meeting Seattle. Nirst Algs. F.Madero, H.Raimondo 29 of 34 July 19-21, 2010 Geometric Corrections

30 6th Aquarius/SAC-D Science Meeting Seattle. Nirst Algs. F.Madero, H.Raimondo 30 of 34 July 19-21, 2010 Goals The objetives of the corrections are: To be able to obtain the latitude, longitude, and other earth location information, for each pixel in an image, with the best accuracy at hand To register the band to a reference band, in order to satisfy science requirements (derived products input). To resample the bands to a given Map Projection.

31 6th Aquarius/SAC-D Science Meeting Seattle. Nirst Algs. F.Madero, H.Raimondo 31 of 34 July 19-21, 2010 Earth Location Parameters Plenty earth location parameters are provided: latitude, longitude, range to spacecraft, azimuth and zenith angles to spacecraft, sun, and moon. Processor inputs (attitude and ephemeris data, mirror position) are validated, and when suitable, interpolated. Using geometric auxiliar data, such as line of sight vectors measured at GEMA, and alignment matrices measured at Brasil. The methods used try to obtain the best available accuracy by using systematic methods. So all the needed precession, nutation, polar wander calculations are considered. A geometric budget error analysis was done before designing the algorithms. From it, it was considered as a good option to use an earth intersection algorithm based on DEM, which is currently being developed at prototype level. The parameters are disposed on a grid, in order to have less computing requirements, while maintaining good accuracy. This grid is later used in the resampling stages.

32 6th Aquarius/SAC-D Science Meeting Seattle. Nirst Algs. F.Madero, H.Raimondo 32 of 34 July 19-21, 2010 Inter-Band Registration and Resampling Inter band registration by using geoloc data, resampling the other bands to the geoloc of the reference band. Resampling based on a partition of the input space in cells (using the grid of the geoloc), and calculating forward and reverse transformations for each cell, between geodetic coordinates and projected coordinates. Transformations calculated using Singular Value Decomposition methods. Interpolation currently using NN, Bilinear and CC. Considering using reconstruction based on a MTF. Map Projections: as provided by proj4. Currently using UTM, and GK-AR.

33 6th Aquarius/SAC-D Science Meeting Seattle. Nirst Algs. F.Madero, H.Raimondo 33 of 34 July 19-21, 2010 Product Format

34 6th Aquarius/SAC-D Science Meeting Seattle. Nirst Algs. F.Madero, H.Raimondo 34 of 34 July 19-21, 2010 Product formats  Processor output: XML files.  CUSS will have libraries and tools to automatically generate (from XML files) products in HDF5, and other, formats.  CUSS will pack the products using any packing format (rar, zip, gz, tar, etc). The contect of the packet file will be:  A folder with the product (XML, HDF5, GeoTiff),  The associated metadata in XML format  Any other needed data such as calibration files, and auxiliary data files.

35 6th Aquarius/SAC-D Science Meeting Seattle. Nirst Algs. F.Madero, H.Raimondo 35 of 34 July 19-21, 2010 END

36 6th Aquarius/SAC-D Science Meeting Seattle. Nirst Algs. F.Madero, H.Raimondo 36 of 34 July 19-21, 2010 Datos de Ciencia y Datos suplementarios Datos de Ciencia y Datos suplementarios

37 6th Aquarius/SAC-D Science Meeting Seattle. Nirst Algs. F.Madero, H.Raimondo 37 of 34 July 19-21, 2010 NIRST – CSDP (CONAE Science Data Packet) --SACAR

38 6th Aquarius/SAC-D Science Meeting Seattle. Nirst Algs. F.Madero, H.Raimondo 38 of 34 July 19-21, 2010 Frame of NIRST 512 pix * 3 ch * 2 By= 3072 Bytes 3072 + 64 +2 = 3138 Bytes Tensiones, corrientes y temperaturas(4 8 bytes) 32 posiciones * 2 By = 64 Bytes Configuración, modos de operación y estado del instrumento (16 bytes) La trama de HK está compuesta por 64 by de los cuales, los primeros 48 (posiciones 0 a 23) están dedicados al almacenamiento de los sensores de: temperaturas (8 posiciones), tensiones (8 posiciones) y corrientes (8 posiciones). Los 16 By restantes (posiciones 24 a 31) están dedicados a la configuración y modos de operación del instrumento.

39 6th Aquarius/SAC-D Science Meeting Seattle. Nirst Algs. F.Madero, H.Raimondo 39 of 34 July 19-21, 2010 HK – Temperaturas de las opticas ver P0 P2000_1MWIR barrel[C] P1 P2000_2Optical bench [C] P2 P2000_3Radiator [C] P3 P2000_4LWIR barrel[C] P4 PKG_MWIRMWIR package P5 HS_MWIRMWIR heat sink[C] P6 PKG_LWIRLWIR package P7 HS_LWIRLWIR heat sink[C] La temperatura de operación de NIRST se mantendrá entre 10 y 18 ºC. Cuando las ópticas superan los 18 ºC o bajan de 10 ºC los canales de 10.85 µm y 11.85 µm comienzan a desenfocar. Las temperaturas a tener en cuenta para este efecto son: las temperaturas de los barriles MWIR y LWIR que se miden con los sensores de temperatura 1 (P0) y 4 (P3) (respectivamente) en la telemetría que envía el instrumento. Por otro lado, plataforma, también lee y envía estos datos en su telemetría y en este caso se denominan: T3= LWIR TEMP y T5= MWIR TEMP. Las primeras 8 posiciones (en el HK) corresponden a las 8 temperaturas que se miden en el instrumento: En los primeros cuatro canales de temperatura En los segundos cuatro canales de temperatura

40 6th Aquarius/SAC-D Science Meeting Seattle. Nirst Algs. F.Madero, H.Raimondo 40 of 34 July 19-21, 2010 Registro Conf ver Selección de potencia del DVF - Conf1(4:2): Conf1(4): Habilitación DVF. Conf1(3): Selección de potencia 2,5 W. Frecuencia de reloj de operación de la ROIC - Conf2(9:2): Modo de operación - Conf1(1:0): Conf1(1:0)="00": Adquisición en modo test digital. Conf1(1:0)="10": Adquisición en modo test analógico. Conf1(1:0)="01": Adquisición en modo observación. Conf(9:2)Hz 0x5 0x6 0x7 0x8 0x9 0x10 2000000 1714285,714 1500000 1200000 1000000 800000 (Read Out Integrated Circuit) % Integración – Conf3: Integ MHz 25 [%] 50 [%] 75 [%] 100 [%] 0.80x3e80x7d00xbb80 10x4e80x9c40xea60 1.20x5dc0xbb80x11940 1.50x7530xea60x15f90 1.7140x85e0x10bd0x191b0 20x9c40x13880x1d4c0

41 6th Aquarius/SAC-D Science Meeting Seattle. Nirst Algs. F.Madero, H.Raimondo 41 of 34 July 19-21, 2010 Mirror Position

42 6th Aquarius/SAC-D Science Meeting Seattle. Nirst Algs. F.Madero, H.Raimondo 42 of 34 July 19-21, 2010 Mirror Position - Comands “La acción de apuntamiento contiene dos operaciones posibles, GOTO la cual tiene la finalidad de llevar el espejo a una posición deseada, y la operación HOME, utilizada para calibrar la posición inicial, ante una eventual "power cycle“ del instrumento. Posteriormente a partir de esta posición se contarán pulsos de avance para registrar la posición de espejo”. “Ambas operaciones se definen con el comando 45h, al enviar este comando se modificar 2 registros ubicados en la FPGA, NREF el cual define la posición que se desea alcanzar (en pasos), y NPOS que registra la posición instantánea (a medida que el espejo avanza). El motor llegará a la posición deseada cuando NPOS sea igual a NREF”.  NIRST_CMD_MIRROR_SPEED CMDVelocidad [ms/paso] 0x02 0x47 0x00 0x00 0x45 0x03(0 +1) * 100 = 100(Opción default) 0x02 0x47 0x07 0x00 0x42 0x03(7 +1) * 100 = 800 0x02 0x47 0x0f 0x00 0x4a 0x03(15+1) * 100 = 1600  NIRST_CMD_POINTING_POSITION_CONTROL

43 6th Aquarius/SAC-D Science Meeting Seattle. Nirst Algs. F.Madero, H.Raimondo 43 of 34 July 19-21, 2010 Mirror Position - Configuration Registers ver El movimiento y posición del espejo se conocen mediante los siguientes registros de configuración: Registro Conf2: Conf2(12:9): Velocidad de apuntamiento. El valor por defecto 0 equivale a 100 ms por pulso. Nota: El seteo del comando 45 (slide anterior) se refleja en este registro. Registro Conf4: Conf4(8:0)= Posición de referencia del espejo (NREF). Registro Conf7: Los 9 bit menos significativos de este registro conf7(8:0) está dedicado a indicar la posición, en pulsos, a la cual se encuentra el espejo. (NPOS). Es la posición en la que se encuentra el espejo.

44 6th Aquarius/SAC-D Science Meeting Seattle. Nirst Algs. F.Madero, H.Raimondo 44 of 34 July 19-21, 2010 Lines of µbolometers selected ver Registro Conf6: Registro que indica cual de las 6 líneas de sensores se han seleccionado para la adquisición de datos. Conf6(2:0): Selección channel 1. Conf6(5:3): Selección channel 2. Conf6(8:6): Selección channel 3. La selección de las líneas se realiza de acuerdo con la siguiente tabla: Default flight configuration: Conf6(2:0) (ch1) = ox4(MWIR2) Conf6(5:3) (ch2) = ox1(LWIR2) Conf6(8:6) (ch3) = ox2(LWIR3)

45 6th Aquarius/SAC-D Science Meeting Seattle. Nirst Algs. F.Madero, H.Raimondo 45 of 34 July 19-21, 2010 Datos de ciencia Los datos entregados por el cabezal óptico se encuentran digitalizados en 15 bits con formato módulo y signo. Estos datos son almacenados en una memoria de 16 bits de longitud para su posterior transmisión a la computadora PAD. Por lo que el bit más significativo (MSB=bit 15), es rellenado con el valor por defecto ’0’. Los datos entregados por el instrumento no corresponde a un valor de cuenta digital, el mismo está codificado con la ecuación re-cursiva 1.6, por lo que para obtener el valor es necesario decodificar cada dato correspondiente a cada pixel utilizando una tabla de conversión (LUT) provista por INO.

46 6th Aquarius/SAC-D Science Meeting Seattle. Nirst Algs. F.Madero, H.Raimondo 46 of 34 July 19-21, 2010 Datos de Radiometría

47 6th Aquarius/SAC-D Science Meeting Seattle. Nirst Algs. F.Madero, H.Raimondo 47 of 34 July 19-21, 2010 LUT – Numerical Evaluation -- SACAR L S (T) [W/m 2.sr] Tb [Kº]... 600...…

48 6th Aquarius/SAC-D Science Meeting Seattle. Nirst Algs. F.Madero, H.Raimondo 48 of 34 July 19-21, 2010 ATBD Radiométrico

49 6th Aquarius/SAC-D Science Meeting Seattle. Nirst Algs. F.Madero, H.Raimondo 49 of 34 July 19-21, 2010 Radiometría – Modelo sencillo Φd = Ls* Ad ┴ * Ωs = Ls * Ad.cos θ*As.cos θ/(r.sec θ) 2 Φd = (Ls.As.Ad / r 2 ) * cos 4 θ Φd = Ls* As ┴ * Ωd = Ls * As.cos θ*Ad.cos θ/(r.sec θ) 2 Φd = (Ls.As.Ad / r 2 ) * cos 4 θ Transferencia de flujo entre una fuente de energía de superficie As y un receptor o detector de área Ad. As y Ad son paralelos. Área aparente o proyectada

50 6th Aquarius/SAC-D Science Meeting Seattle. Nirst Algs. F.Madero, H.Raimondo 50 of 34 July 19-21, 2010 Radiometría – Modelo mas complejo Φ = Lobj * Aobj * Ωlente desde obj Φ = Lobj * Aimg * Ωlente desde img Φ = Lobj * Alent * Ωobj - 1 - Φ = Lobj * Alent * Ωimg - 2 - La ultima ecuación se lee: El flujo que llega hasta el plano de imagen (al detector) es la misma que si tuviésemos una fuente del tamaño de la lente (del Área del diafragma de apertura de la óptica) y con una radiancia igual a la del objeto (píxel de tierra). Transferencia de flujo [W] entre una fuente de energía de superficie Aobj y un receptor o detector ubicado en el plano imagen.

51 6th Aquarius/SAC-D Science Meeting Seattle. Nirst Algs. F.Madero, H.Raimondo 51 of 34 July 19-21, 2010 NIRST – Apunt. Nadiral y Lateral

52 6th Aquarius/SAC-D Science Meeting Seattle. Nirst Algs. F.Madero, H.Raimondo 52 of 34 July 19-21, 2010 Transf. de flujo – Visión Nadiral (Por comodidad del dibujo suponemos que la cámara esta rotada un ángulo β = 7.665 dgr ) Si adaptamos la ecuaci ó n 2 (disp 10) a la nomenclatura de la Figura Visi ó n Nadiral, podemos plantear la ecuaci ó n general de flujo que llega a cualquier detector individual dentro del sensor: Φd = Ls * Ada θ┴ * Ωd θ = Para el pixel central (θ = 0): Φd(0) = Ls * Ada * Ωd 0 = Ls* Ada * Ad / f 2 = Φ 0 - 3 - Para un pixel lateral (θ ≠ 0) (ecuaci ó n general): Φd(θ)= Ls * Ada θ┴ * Ωp θ = Ls* Ada.cos θ * Ad. cos θ / (f 2. sec 2 θ) = Ls* Ada * Ad/ f 2. cos 4 θ = Φ 0 * cos 4 θ- 4 - La irradiancia sobre los detectores ser á : Ed(0) = Φd(0) / Ad = Ls * Ada / f 2 = E 0 Ed(θ)= Φd(θ) / Ad = (Ls * Ada / f 2 )* cos 4 θ = E 0 * cos 4 θ Vemos que el flujo transferido a los detectores (y la irradiancia sobre los mismos) disminuye con el cos 4 θ.

53 6th Aquarius/SAC-D Science Meeting Seattle. Nirst Algs. F.Madero, H.Raimondo 53 of 34 July 19-21, 2010 Transf. de flujo – Visión Nadiral Estas ecuaciones son validas si consideramos a la tierra como una superficie Lambertiana e Isotrópica, esto es un cuerpo que presenta (refleja/emite) una radiancia L que es independiente del ángulo de observación. Es decir, si se tiene un cuerpo con una irradiancia uniforme, la irradiancia sobre los detectores seria como se muestra en la figura siguiente:

54 6th Aquarius/SAC-D Science Meeting Seattle. Nirst Algs. F.Madero, H.Raimondo 54 of 34 July 19-21, 2010 Transf. de flujo – Visión Lateral Si nuestro modelo son: Modelo Atmosfera: ideal (sin absorci ó n, sin dispersi ó n, sin emisi ó n atmosf é rica), al sensor llegara toda la energ í a proveniente de la fuente (superficie emisora) y solamente esa energ í a ( atenuación del camino atmosférico = 0). Modelo de superficie: Superficie Lambertiana (en el rango visible) y emisor Isotr ó pico en el infrarrojo. En estas condiciones, si observamos ahora los mismos pixeles del terreno pero con una visi ó n lateral (tal como se muestra en la Figura Visi ó n Lateral, seguir á n siendo validas las ecuaciones 3 (para el p í xel central) y 3 (para pixeles laterales). En efecto, si analizamos las ecuaciones 3 y 4: Φd(0) = Ls * Ada * Ad / f 2 = Φ 0 Φd(θ) = Ls * Ada * Ad/ f 2. cos 4 θ = Φ 0 * cos 4 θ Puede verse que: Ada, Ad, f y θ son los mismos tanto en visi ó n nadiral como en visi ó n lateral, est á n fijados por la geometr í a del conjunto sensor- ó ptica. Y si los pixeles observados en ambas condiciones (visi ó n nadiral y visi ó n lateral) pertenecen a una superpie Lambertiana y/o emisor Isotr ó pico, Ls tambi é n ser á la misma en cualquier condici ó n/direcci ó n de observaci ó n.

55 6th Aquarius/SAC-D Science Meeting Seattle. Nirst Algs. F.Madero, H.Raimondo 55 of 34 July 19-21, 2010 NIRST – Ecuación Radiométrica

56 6th Aquarius/SAC-D Science Meeting Seattle. Nirst Algs. F.Madero, H.Raimondo 56 of 34 July 19-21, 2010 NIRST – Ecuación Radiométrica

57 6th Aquarius/SAC-D Science Meeting Seattle. Nirst Algs. F.Madero, H.Raimondo 57 of 34 July 19-21, 2010 ATBD Geometrico