> **LANDSAT DATA CONTINUITY**
>
> **MISSION**

**Operational Land Imager (OLI) /**

> **National Polar Operational Environmental Satellite System (NPOESS)
> 2130 Spacecraft Interface Requirements**
>
> **April 18, 2005**

![](media/image1.png)

**[Signature Page]{.underline}**

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**LDCM PROJECT**

**DOCUMENT CHANGE RECORD**

Sheet: 1 of 1

+------------+----------------------------------------------+---------+
| REV        | DESCRIPTION OF CHANGE                        | DATE    |
|            |                                              |         |
| LEVEL      |                                              | A       |
|            |                                              | PPROVED |
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|            |                                              |         |
+------------+----------------------------------------------+---------+

**TABLE OF CONTENTS**

> [Page]{.underline}

[1 OLI / NPOESS GIID Compliance 1-1](#oli-npoess-giid-compliance)

[2 OLI / NPOESS Mass, Volume, and Power Accommodation
2-1](#oli-npoess-mass-volume-and-power-accommodation)

[3 OLI / NPOESS Field of View Accommodation
3-3](#oli-npoess-field-of-view-accommodation)

[3.1 Nadir Field of View 3-3](#nadir-field-of-view)

[3.1.1 Unobstructed Field of View 3-3](#unobstructed-field-of-view)

[3.1.2 Glint-Free Field of View 3-3](#glint-free-field-of-view)

[3.2 Solar Calibration Field of View
3-4](#solar-calibration-field-of-view)

[3.2.1 Unobstructed Field of View 3-4](#unobstructed-field-of-view-1)

[3.2.2 Glint-Free Field of View 3-4](#glint-free-field-of-view-1)

[4 NPOESS 2130 Orbit Requirements for OLI
4-5](#npoess-2130-orbit-requirements-for-oli)

[4.1 Orbit Parameters 4-5](#orbit-parameters)

[4.2 Cross-Track Repeat Cycle Variability
4-5](#cross-track-repeat-cycle-variability)

[5 NPOESS OLI Stored Mission Data Interface
5-1](#npoess-oli-stored-mission-data-interface)

[5.1 Operational Concept 5-1](#operational-concept)

[5.2 OLI Stored Mission Data Interface Circuit
5-1](#oli-stored-mission-data-interface-circuit)

[5.3 Mission Data Transfer Timing 5-2](#mission-data-transfer-timing)

[5.4 OLI Mission Data Transfer Interface Data Format
5-3](#oli-mission-data-transfer-interface-data-format)

[5.4.1 OLI Mission Data Packet Format
5-4](#oli-mission-data-packet-format)

[6 OLI Command, Telemetry, Time and Ancillary Data Interfaces
6-1](#oli-command-telemetry-time-and-ancillary-data-interfaces)

[6.1 Command and Telemetry Interfaces
6-1](#command-and-telemetry-interfaces)

[6.1.1 Telemetry Formatting 6-1](#telemetry-formatting)

[6.1.2 Number of Functionally Distinct Instrument Remote Terminals
6-1](#number-of-functionally-distinct-instrument-remote-terminals)

[6.1.3 RT Physical Address Assignment
6-1](#rt-physical-address-assignment)

[6.1.4 OLI Combined Data Bus Rates 6-1](#oli-combined-data-bus-rates)

[6.2 OLI Auxiliary Data Input from NPOESS Spacecraft
6-2](#oli-auxiliary-data-input-from-npoess-spacecraft)

[6.3 OLI Time of Day Input from NPOESS Spacecraft
6-2](#oli-time-of-day-input-from-npoess-spacecraft)

[7 Telemetry and Command Requirements
7-1](#telemetry-and-command-requirements)

[7.1 Command Uploads 7-1](#command-uploads)

[7.2 OLI Non-operational Point to Point Telemetry Interfaces
7-1](#oli-non-operational-point-to-point-telemetry-interfaces)

[7.3 Realtime Monitoring and Autonomous Fault Detection and Correction
7-1](#realtime-monitoring-and-autonomous-fault-detection-and-correction)

[8 NPOESS Disturbance environment at oli instrument interface
8-1](#npoess-disturbance-environment-at-oli-instrument-interface)

[8.1 RBS Alignment Knowledge Uncertainty between Spacecraft Attitude
Determination Frame and the RBS Instrument Interface Reference --
Absolute
8-1](#rbs-alignment-knowledge-uncertainty-between-spacecraft-attitude-determination-frame-and-the-rbs-instrument-interface-reference-absolute)

[8.2 Alignment Knowledge Uncertainty between S/C Attitude Determination
Frame and the RBS Interface Reference (over a 17day Orbital Cycle)
8-1](#alignment-knowledge-uncertainty-between-sc-attitude-determination-frame-and-the-rbs-interface-reference-over-a-17day-orbital-cycle)

[8.3 Alignment Knowledge Uncertainty between S/C Attitude Determination
Frame and the RBS Instrument Interface Reference (over a 30 sec along
track interval)
8-1](#alignment-knowledge-uncertainty-between-sc-attitude-determination-frame-and-the-rbs-instrument-interface-reference-over-a-30-sec-along-track-interval)

[8.4 Disturbance Spectra at the Spacecraft-Instrument Interface
8-1](#disturbance-spectra-at-the-spacecraft-instrument-interface-tbc)

[8.4.1 Spacecraft Rotational Disturbance Environment
8-1](#spacecraft-rotational-disturbance-environment-tbc)

[8.4.2 Spacecraft Linear Disturbance Environment
8-3](#spacecraft-linear-disturbance-environment-tbc)

[9 OLI Point to Point CMD/TLM Interfaces
9-1](#oli-point-to-point-cmdtlm-interfaces)

[9.1 Pulse Commands 9-1](#pulse-commands)

[10 OLI --NPOESS Thermal Interface RequirementS
10-1](#oli-npoess-thermal-interface-requirements)

[10.1 Thermal Fields of View 10-1](#thermal-fields-of-view)

[Appendix A: Disturbance Sensitivity Curves
1](#appendix-a-disturbance-sensitivity-curves)

**LIST OF FIGURES**

[Figure]{.underline} [Page]{.underline}

**LIST OF TABLES**

[Table]{.underline} [Page]{.underline}

> [Table 2‑1 OLI Mass / Volume / Power NTE Envelopes
> 2-1](#__RefHeading___Toc101326033)
>
> [Table 6‑1 NPOESS Spacecraft Ancillary Data Update Rate and Accuracy
> for OLI Interface 6-2](#__RefHeading___Toc101326034)

**OLI / NPOESS 2130 SPACECRAFT INTERFACE REQUIREMENTS**

# OLI / NPOESS GIID Compliance

Unless otherwise stated in the sections below, the OLI shall comply with
all current requirements in the NPOESS General Instrument Interface
Document (GIID), Doc. No. D31418 Rev. B (in bidders' library)

# OLI / NPOESS Mass, Volume, and Power Accommodation 

The NPOESS 2130 Spacecraft shall accommodate an OLI that meets the
not-to-exceed (NTE) mass, volume, and power interface envelopes for
those values specified in Table 2-1 (volume envelopes illustrated in
Figure 2-1) and in the candidate location indicated in Figure 2-2.

Calibration deployed volume shall occur no more than 20 (TBR) continuous
minutes in duration nominally once per week. Shorter duration temporary
exceedences of the stowed / operational volume shall be negotiated
between the OLI and NPOESS contractors on a case-by-case basis.

The stowed volume does not preclude placement of other OLI subsystems
(e.g. DSAP) within the NPOESS 2130 spacecraft if feasible (to be
negotiated with IPO/ NGST).

+-------+--------+--------------+-------------+-----------+-----------+
|       | **     | **Stowed /   | **          | **Average | **Peak    |
|       | Mass** | Operational  | Calibration | Orbital   | Power**   |
|       |        | Volume**     | Deployed    | Power**   |           |
|       |        |              | Volume**    |           |           |
|       |        |              |             |           |           |
|       |        |              | **(TBC)**   |           |           |
+-------+--------+--------------+-------------+-----------+-----------+
| **OLI | 400kg  | 1.5m (z)     | 2.0m (z) by | 425 Watts | 510 Watts |
| To    | **(    | **(TBC)** by | 1.2m (x) by |           |           |
| tal** | TBC)** | 1.2m (x) by  | 1.2m (y)    |           |           |
|       |        | 1.2m (y)     |             |           |           |
|       |        | (see figures |             |           |           |
|       |        | 2-2 and 2-3  |             |           |           |
|       |        | below)       |             |           |           |
+-------+--------+--------------+-------------+-----------+-----------+

[]{#__RefHeading___Toc101326033 .anchor}Table 2‑1 OLI Mass / Volume /
Power NTE Envelope

![](media/image2.wmf){width="5.19375in" height="3.725in"}

Figure 2-1 Illustration of OLI Stowed / Deployed Volume Envelopes

![](media/image3.wmf){width="3.6319444444444446in"
height="3.3680555555555554in"}

Figure 2-2 Candidate Location for OLI on NPOESS 2130 Spacecraft

# OLI / NPOESS Field of View Accommodation

####  {#section .unnumbered}

## Nadir Field of View

### **Unobstructed Field of View**

####  {#section-1 .unnumbered}

#### The NPOESS 2130 Spacecraft shall provide an unobstructed minimum nadir field of view for OLI which provides a 12.9 degree cross track width by at least 1.7 degree along track length. (Figure 3-1, left) {#the-npoess-2130-spacecraft-shall-provide-an-unobstructed-minimum-nadir-field-of-view-for-oli-which-provides-a-12.9-degree-cross-track-width-by-at-least-1.7-degree-along-track-length.-figure-3-1-left .unnumbered}

### Glint-Free Field of View

The NPOESS 2130 Spacecraft shall provide the OLI an unobstructed FOV
within a conical **25° (TBC)** half angle of optical nadir to minimize
collection of scattered energy. The cone's circular intersection on the
+Z face shall envelope the oval-shaped nadir port aperture. (Figure 3-1,
right).

![](media/image4.wmf){width="6.404166666666667in" height="4.14375in"}

**Figure 3-1 OLI Unobstructed (Left) and Glint-Free (Right) Nadir Fields
of View**

## Solar Calibration Field of View

### Unobstructed Field of View

The NPOESS 2130 Spacecraft shall provide the OLI with a solar
calibration field of view unobstructed by spacecraft structures for any
time of the year across a range of solar elevation angles from **-15° to
-25° (TBC)** relative to the local horizontal for either the post
eclipse exit portion of the orbit (for a forward facing solar diffuser)
or the pre eclipse entrance portion of the orbit (for an aft facing
solar diffuser).  To cover the seasonal variation in the solar azimuthal
position, the clear solar calibration field of view for the indicated
solar elevation range shall be **38°± 8° (TBC)** in azimuth towards the
sun side from the velocity vector or anti-velocity vector, respectively,
for the post eclipse exit or pre-eclipse entrance portions of the
orbit.  (Figure 3-2, left)

### Glint-Free Field of View

The NPOESS 2130 Spacecraft shall provide the OLI an unobstructed FOV
within a region bounded by **--10 to --30° (TBC)** in elevation and
**38°± 60°** **(TBC)** in azimuth (towards the sun side) from the edges
of the solar calibration port. The bounding surface of this region's
intersection with the instrument shall envelope the rectangular shaped
solar calibration aperture. (Figure 3-2, right).

![](media/image5.wmf){width="6.5125in" height="3.859722222222222in"}

**Figure 3-2 OLI Unobstructed (Left) and Glint-Free (Right) Solar
Calibration Fields of View**

# NPOESS 2130 Orbit Requirements for OLI 

## Orbit Parameters 

The NPOESS 2130 Spacecraft shall operate the OLI in a geodetically
pointed 828km +/-12km near circular sun synchronous orbit with a 17 day,
241-path repeatable ground track orbit inclined by 98.7 degrees with an
equatorial ascending node crossing time of 2130hrs (+/- 10 minutes).

## Cross-Track Repeat Cycle Variability

The NPOESS 2130 orbit cross-track repeat variability for the orbit
defined in section 4.1 above shall not exceed +/-5 km per 17 day cycle.

# NPOESS OLI Stored Mission Data Interface

## Operational Concept

NPOESS 2130 S/C transmits Stored Mission Data via a Ka-Band downlink to
globally distributed ground receptor sites during the course of an
orbit. The ground periodically uploads an SMD contact schedule
(providing start times and durations for NPOESS and OLI access to the
SMD downlink) good for 48 hours into the future. OLI access to the SMD
downlink will be scheduled such that it will see an average transmission
rate (over a 24-hour period) no less than 23 Mbps.

When it is OLI's turn to transmit SMD, as directed by the onboard
contact schedule, a command will be sent by the S/C via the 1553B data
bus activating the OLI Stored Mission Data Interface. Once activated,
OLI monitors the state of a hardwired Ready signal (RCV_RDY, see below)
and transfers a block of data each time the Ready signal transitions to
a true state.

The OLI Stored Mission Data interface protocol is designed to allow
transmission at a continuous 150 Mbps. Should OLI not respond to the
Ready signal in a timely enough fashion, the S/C will insert a fill
block into the downlink so as to maintain link data continuity. OLI's
next transmission opportunity will occur following transmission of the
fill block. At the end of the scheduled OLI SMD contact period, the S/C
will no longer activate the Ready signal thus inhibiting further data
transfer. A command will be sent by the S/C to OLI via the 1553B data
bus deactivating the OLI Stored Mission Data interface.

## OLI Stored Mission Data Interface Circuit

The OLI Mission Data Interface circuits shall comply with Low Voltage
Differential Signal (LVDS).

The OLI Mission Data Interface configuration shall be as depicted in
Figure 5-1.

The OLI Mission Data Interface signals shall consist of prime and
redundant signals designated as RCV_RDY_X/, DATA(7:0)\_X, DATA_CLK_X and
ENABLE_X/ where the X in each signal name corresponds to either A or B
depending upon the primary or redundant signal designation.

![](media/image6.wmf){width="5.051388888888889in"
height="4.301388888888889in"}

**Figure 5-1 OLI Mission Data Interface Circuits**

## Mission Data Transfer Timing

Activation and deactivation of OLI Mission Data transfer shall be
commanded via the 1553B data bus interface.

OLI Mission Data interface activation and deactivation commands shall be
processed in OLI such that data transfers start and stop on block
boundaries.

When OLI Mission Data Transfer is activated, data shall be transferred
as a 1024 byte block, 8-bits (DATA(7:0)) per DATA_CLK, enveloped by the
ENABLE signal for each inactive to active RCV_RDY transition. Note: The
RCV_RDY may transition true prior to completion of the current block
transfer.

The DATA_CLK signal shall be a 50% duty cycle square wave at 20 MHz.

OLI Mission Data Transfer Timing shall be as depicted in Figure 5-2.

The Delay from activation of RCV_RDY_X/ to start of data transmission
shall be 1 us or less. Delays greater than 1us may result in the
insertion of a fill block into the SMD downlink. Inserted fill blocks
are considered part of the 23 Mbps rate allocation.

![](media/image7.wmf){width="5.997222222222222in"
height="1.4465277777777779in"}

**Figure 5-2 OLI Mission Data Transfer Timing**

## OLI Mission Data Transfer Interface Data Format

Each 1024 byte Data Block transferred via the OLI Mission Data interface
shall be formatted as depicted in Figure 5-3.

![](media/image8.wmf){width="5.995833333333334in" height="1.10625in"}

**Figure 5-3 OLI Mission Data Interface Data Format**

The fields within the format depicted in Figure 5-3 shall be correspond
to an Interleave Depth 4, CCSDS Channel Access Data Unit as specified in
CCSDS 701.0-B-2, Advanced Orbiting Systems, Networks and Data Links,
except as noted below.

The S/C ID field shall be as specified in NPOESS Reference Document
D35853, NPOESS Data Mapping APID, VCID, Downlink and Uplink.

The Virtual Channel ID field shall be as specified in NPOESS Reference
Document D35853, NPOESS Data Mapping APID, VCID, Downlink and Uplink.

OLI shall be capable of modifying the assigned S/C ID and VCID values
without disassembly.

The 24-bit Virtual Channel Data Unit Counter field shall be lengthened
by eight bits using the VCDU Counter Extension field resident in the
Insert zone.

The VCDU Counter Extension field shall form the MSBs of the total 32-bit
Virtual Channel Data Unit Counter.

The Replay Flag shall not be used and set to '0'.

Spare fields shall be set to '0's.

The First Header Pointer field shall be set per CCSDS 701.0-B-2,
Advanced Orbiting Systems, Networks and Data Links.

The MPDU Packet zone shall contain multiplexed OLI Mission Data Packets.

### OLI Mission Data Packet Format

The OLI Mission Data Packet shall be formatted per CCSDS 701.0-B-2 and
301.0-B-2 using the CCSDS path Protocol Data Unit (CP_PDU) format (also
known as Version 1 Source Packet.

OLI Mission Data Packet size shall be limited to no more than 65,507
bytes including all headers.

OLI Mission Data Packets shall be formatted with an Application Process
ID value(s) of [TBD]{.mark}.

# OLI Command, Telemetry, Time and Ancillary Data Interfaces

## Command and Telemetry Interfaces

The NPOESS / OLI Command and Telemetry interface shall be MIL-STD-1553B
interface in compliance with the requirements in NPOESS reference
document D34470, NPOESS 1553 Interface Requirements Document except as
tailored in the subsections below.

### Telemetry Formatting

The 1553B interface shall be utilized for the transfer of Test, Memory
Dump, Dwell, Housekeeping, LEO&A and Telemetry Monitor packets types (if
utilized) specified in D34470, NPOESS 1553 Interface Requirements
Document.

Engineering, Calibration, Diagnostic and Science packet types shall not
be transferred via 1553B.

### Number of Functionally Distinct Instrument Remote Terminals

OLI shall have no more than two dual redundant RT interfaces coupled to
the data bus.

### RT Physical Address Assignment

OLI's RT physical addresses shall be assigned as [TBD]{.mark}.

### OLI Combined Data Bus Rates

Peak data rates for OLI to S/C data transfers on the 1553B data bus
shall not exceed 2.048 kbps.

Should there be higher rate data transfers required, those higher rate
data types will be transferred via the OLI Stored Mission Data
Interface.

Peak data rates on the 1553B bus for S/C to OLI data transfers
(Commands, Time of Day, Ancillary and Uploads) shall not exceed
[TBD]{.mark} bps.

It is recommended that OLI be designed to accept an input rate up to 128
kbps for commands and uploads. This rate assumes that the entire uplink
rate in a given uplink contact period is dedicated to OLI. The actual
input rate will be a function of how much of an uplink contact is
allocated to OLI versus NPOESS.

## OLI Auxiliary Data Input from NPOESS Spacecraft

The NPOESS 2130 spacecraft Command and Data Handling System shall
provide the OLI with periodic auxiliary data at the specified update in
Table 6-1. Detailed auxiliary data contents and formatting shall be
defined in the OLI-NPOESS 2130 ICD.

  ----------------- ----------------- ----------------- -----------------
  **Spacecraft      **Minimum Update  **Accuracy 3      **Accuracy of
  Parameter**       Rate**            sigma**           Time Correlation
                                                        to GPS Time, 3
                                                        sigma**

  Measured attitude 5.0Hz             15 arc-sec        48 microsec
  with respect to                                       
  body frame                                            

  Individual gyro   32hz              2.25 arc-sec over 48 microsec
  axis rate data                      30 sec window     

  RT Ephemeris      1.0 Hz            30m               48 microsec
  Calculation                                           
  ----------------- ----------------- ----------------- -----------------

[]{#__RefHeading___Toc101326034 .anchor}Table 6‑2 NPOESS Spacecraft
Ancillary Data Update Rate and Accuracy for OLI Interface

## OLI Time of Day Input from NPOESS Spacecraft

The NPOESS / OLI Time of Day interface shall be as specified in NPOESS
reference document D34470, NPOESS 1553 Interface Requirements Document
except as tailored below.

The Time of Day sent in the TOD packet shall correspond to international
standard UTC time at the occurrence of the TOD pulse +/- [200 us
TBD]{.mark}.

# Telemetry and Command Requirements

## Command Uploads

The OLI-NPOESS spacecraft command interface shall support daily command
uploads from the of NPOESS MOC command sequences which provide
autonomous operations of the OLI for 48hour periods

## OLI Non-operational Point to Point Telemetry Interfaces

The OLI-NPOESS Spacecraft interface shall provide real-time monitoring
of critical OLI instrument health and safety parameters during periods
where the instrument is non-operational (powered off)

## Realtime Monitoring and Autonomous Fault Detection and Correction

The NPOESS 2130 spacecraft shall provide real-time monitoring and
autonomous fault detection and correction of critical OLI health and
safety telemetry of the OLI whether operationally powered on or powered
off.

OLI shall provide to the S/C all monitor points requiring real-time
monitoring in a standalone TMON Packet.

OLI shall provide to the S/C the autonomous fault response algorithm for
each TMON monitor point.

# NPOESS Disturbance environment at oli instrument interface

## RBS Alignment Knowledge Uncertainty between Spacecraft Attitude Determination Frame and the RBS Instrument Interface Reference -- Absolute

The NPOESS / OLI interface shall ensure that the alignment between the
NPOESS 2130 spacecraft attitude determination frame and the RBS
instrument interface shall be known to an accuracy of 75 arc-sec
(3-sigma), or less. Prelaunch alignment knowledge data shall be provided
by the spacecraft contractor.

## Alignment Knowledge Uncertainty between S/C Attitude Determination Frame and the RBS Interface Reference (over a 17day Orbital Cycle)

The NPOESS / OLI interface shall ensure that the alignment between the
NPOESS 2130 spacecraft attitude determination frame and the RBS
instrument interface shall be known to within 40 arc-sec (3-sigma) or
less over a period of 17 days.

###  {#section-2 .unnumbered}

## Alignment Knowledge Uncertainty between S/C Attitude Determination Frame and the RBS Instrument Interface Reference (over a 30 sec along track interval) 

The NPOESS / OLI interface shall be such that the alignment between the
NPOESS 2130 spacecraft attitude determination frame and the RBS
instrument interface, including the effects of jitter, shall be stable
to within 40 arc-sec (3-sigma) or less over a period of 30 seconds.

## Disturbance Spectra at the Spacecraft-Instrument Interface (TBC)

This section provides sensitivity functions that relate the disturbance
imparted by the spacecraft at the spacecraft-instrument interface, to
the instrument data quality metrics of image smear and row-to-row
sampling error.

### Spacecraft Rotational Disturbance Environment (TBC)

The combined effects of rotational and linear (see section 8.4.2)
disturbances in all axes from the NPOESS 2130 spacecraft shall
contribute an RSS of less than 7.2 microradians in each axis after
multiplication by the transfer functions of Figure 8-1 and Figure 8-2.
This RSS is computed by weighting the spacecraft rotational and linear
disturbance spectra between 0.01 Hz and 1000 Hz by the instrument
sensitivity transfer functions and integrating.

![](media/image9.png){width="5.997222222222222in"
height="4.101388888888889in"}Figure 8-1 Sensitivity to the Spacecraft
Rotational Disturbance Environment (TBC)

### Spacecraft Linear Disturbance Environment (TBC)

The combined effects of rotational (see section 8.4.1) and linear
disturbances in all axes from the NPOESS 2130 spacecraft shall
contribute an RSS of less than 7.2 microradians in each axis after
multiplication by the transfer functions of Figure 8-1 and Figure 8-2.
This RSS is computed by weighting the spacecraft rotational and linear
disturbance spectra between 0.01 Hz and 1000 Hz by the instrument
sensitivity transfer functions and integrating.

![](media/image10.png){width="5.997222222222222in"
height="4.101388888888889in"}Figure 8-2 Sensitivity to the Spacecraft
Linear Disturbance Environment (TBC)

# OLI Point to Point CMD/TLM Interfaces

The NPOESS / OLI Command and Telemetry point to point interfaces shall
comply with the requirements in NPOESS reference document D31418, NPOESS
General Instrument Interface Document except as tailored in the
subsections below.

## Pulse Commands

OLI shall require no more than 6 (six) pulse command interfaces.

The Logic one state pulse command voltage shall be 20V min \@350 mA load
sink current.

# OLI --NPOESS Thermal Interface RequirementS

## Thermal Fields of View 

The NPOESS 2130 spacecraft shall provide accommodation not to exceed
[TBD]{.mark} square meters of OLI Thermal radiators as mutually agreed
to by the OLI and NPOESS 2130 Spacecraft Contractors. This area shall be
located 1) as close as possible to the +Y (cold) edge of the spacecraft
structure and 2) in the spacecraft X-Z plane.  This area shall have a
minimally obstructed (TBR) hemispherical FOV. Actual area shall be
negotiate\
\
Thermal analysis shall verify the heat transfer adequacy of the final
mounting location.  Details of adjacent hardware within the OLI thermal
FOV shall be provided by the spacecraft to a mutually agreed upon level
of fidelity.

## Appendix A: Disturbance Sensitivity Curves {#appendix-a-disturbance-sensitivity-curves .unnumbered}

The sensitivity curves shown in section 8.4 were derived by combining an
assumed isolation system transfer function, **G**isolator(ω), with image
quality sensitivity functions, **G**sensitivity(ω), based on assumed
instrument characteristics. This is shown in figure A-1.

![](media/image11.wmf){width="5.998611111111111in"
height="0.5743055555555555in"}Figure A-1 Relating Disturbance Input to
Performance Metrics

The isolator model used for the curves in section 8.4 is:

$G_{\text{isolator}}(s) = (\frac{s^{2}}{\omega_{2}^{2}} + 2\zeta_{2}\frac{s}{\omega_{2}} + 1\frac{)}{(}\frac{s^{2}}{\omega_{1}^{2}} + 2\zeta_{1}\frac{s}{\omega_{1}} + 1)$

with:

ω~1~ = 2π \* 10

ω~2~ = 2π \* 100

ζ1 = 0.2

ζ2 = 0.707

The sensitivity function for image smear is:

![](media/image12.wmf){width="4.4534722222222225in"
height="0.7451388888888889in"}with:

ti = 0.0045 seconds (integration time).

The sensitivity function for row-to-row sampling shift is:

![](media/image13.wmf){width="5.127083333333333in"
height="0.9013888888888889in"}with:

tsh = 0.0090 seconds (even-odd detector row delay).

The sensitivity is amplified by internal resonance in the RBS structure.
The model for this is:

$$\begin{array}{r}
G_{\text{resonance}}(\omega) = \ 1\ \omega < \omega_{0} \\
\  = \ Q_{r} \cdot L_{o}\ \omega \geq \omega_{0}
\end{array}$$

with:

ω~0~ = 2π \* 50 = resonant frequency

Qr = 50 = mechanical Q of resonance

Lo = 1.296 = optical lever

The combined sensitivity function is the root-sum-square of the smear
and shift sensitivities with the resonance function applied. The
rotational disturbance sensitivity function used in section 8.4.1 is
thus:

$$G_{\text{sensitivity}}(\omega) = G_{\text{resonance}}(\omega)\sqrt{\left( G_{\text{smear}}(\omega) \right)^{2} + \left( G_{\text{shift}}(\omega) \right)^{2}}$$

The parameter values used here are nominal. Both the functions and the
parameter values must be adjusted to reflect the actual OLI design.