Authored By Mojtaba Falahati, Ethan Keeler
Introduction:
Optical jitter is a key performance concern for CubeSats carrying imaging or optical communication payloads. It refers to high-frequency line-of-sight (LOS) motion caused by onboard disturbances such as reaction wheels, attitude control activity, and structural vibrations. Due to their small size and lightweight construction, CubeSats are especially sensitive to these disturbances, which can excite structural modes and propagate through the optomechanical system, resulting in image blur, pointing errors, or reduced optical throughput.
This knowledgebase article describes a practical simulation workflow for predicting CubeSat optical jitter using ANSYS Mechanical and Zemax OpticStudio. Structural frequency response functions (FRFs) are generated in ANSYS Mechanical to capture how disturbance inputs translate into displacements and rotations at the optical payload. These mechanical responses are then mapped into Zemax model to evaluate the resulting LOS motion and optical performance impact. By combining structural dynamics and optical modeling in a unified analysis flow, users can quantify jitter sensitivity, allocate jitter budgets, and assess mitigation strategies early in the design process.
Method:
The optical jitter analysis starts with a modal analysis of CubeSat in ANSYS Mechanical to identify the structural modes within the frequency range relevant to reaction wheel disturbances (In this example, we only consider the disturbance torque from the reaction wheels which is typically the dominant source of optical jitter.). To determine jitter contributions from the reaction wheels, a harmonic response analysis is performed using unit excitation, with the frequency sweep covering the fundamental disturbance frequency and multiple harmonics derived from the reaction wheel rotational speed. This analysis results in the system frequency response that describes how wheel-induced vibrations propagate through the spacecraft structure to the optical payload.
The resulting structural frequency response data at the optical interfaces are post-processed and exported using a Mechanical APDL script. The mechanical FRFs, together with the reaction wheel input PSD and the Zemax optical model, are then loaded into the STAR Jitter module. STAR Jitter combines structural dynamics and optical sensitivity to compute the line-of-sight (LOS) FRF, LOS output PSD, and jitter-induced modulation transfer function (MTF), enabling direct evaluation of optical performance degradation due to reaction-wheel-driven jitter.
1. Structural Dynamics
Disturbances such as reaction wheel imbalance introduce non-deterministic vibration inputs, for which instantaneous response levels cannot be predicted in time domain. As a result, a statistical description of the system response is required. We assume the vibration environment to be stationary and ergodic, which is typical for spacecraft design analysis. Stationarity implies that the statistical properties of the excitation, such as the mean and standard deviation, remain constant over time, while ergodicity allows time-averaged statistics to be treated as representative of the full response.
Random vibration environments are commonly described in frequency domain using power spectral density (PSD). The random response of a linear system subjected to a PSD input is obtained by multiplying the input PSD by the squared magnitude of the system frequency response. We first compute the frequency response of the CubeSat structure under linearized conditions (constant wheel speed) to determine which modes/frequencies are sensitive. In fact, the frequency response tells you how much the optical payload vibrates per unit torque at each frequency, and the torque disturbance input PSD (harmonics + broadband) tells you how much torque is actually applied by the wheel. For a reaction wheel with a nominal or rated speeds around 6000 rpm, the fundamental disturbance frequency would be 100 Hz, and we expect harmonics at 100, 200, 300, ... Hz. We can consider a typical worst-case reaction-wheel torque PSD as shown below:
To generate the required FRFs, a frequency response (harmonic response) analysis is performed to compute the steady-state dynamic response of the CubeSat structure under oscillatory excitation (unit-amplitude torque at the reaction wheel). The structural frequency response is computed in ANSYS Mechanical using the mode superposition method. In this approach, the structural mode shapes serve as the physical coordinates of the system, allowing the coupled equations of motion to be uncoupled and solved efficiently. The total system response is expressed as a summation of individual modal contributions. Once the equations of motion are solved, frequency response functions are generated to describe the magnitude and phase of the structural response as a function of excitation frequency.
In this study, frequency responses of all nodes at the CubeSat mirrors surfaces are extracted using an APDL post-processing script. The user specifies the desired number of frequencies over the excitation spectrum and the number of time steps per vibration cycle for each frequency (in this example, 30 frequencies and 10 timesteps per cycle for each frequency). ANSYS Mechanical then generates STAR data as the corresponding nodal displacements datasets and writes them to the user file for subsequent integration with the optical jitter analysis.
2. Optical Jitter Analysis Using STAR
The optical jitter analysis is performed using the STAR Jitter module, a standalone executable that combines structural dynamic response data with optical sensitivity of the optical model in Zemax. The purpose of this module is to compute the LOS frequency response function, LOS output PSD, and the resulting jitter-induced degradation in modulation transfer function (MTF).
LOS jitter may be computed either as the transverse motion of the image (image space LOS) or as the angular boresight error which is image motion divided by the effective focal length. LOS jitter in an optical system is not only due to rigid body motion. Both rigid body motion and elastic deformation can contribute. In high-performance systems such as space optics, telescopes, automotive LiDAR, etc., elastic effects can be even more important. STAR takes both into consideration when computing the jitter LOS.
The analysis begins by loading three required inputs:
the Zemax optical design file (ZMX),
the disturbance input PSD (representing reaction wheel excitation), and
the structural frequency response data exported from Ansys Mechanical (STAR data file containing nodal displacement responses).
After loading the data, you need to click "Compute", and STAR starts reading the frequencies over the desired spectrum and the timesteps information for each harmonic frequency from the STAR Data folder. For every frequency and time step, the module loads the optical surfaces deformations onto the lens file and computes the radial centroid motion (using CENX and CENY operands) of the spot at the image surface due to the structural deformations inputs. The spot centroid shifts represent the instantaneous image motion caused by structural vibration. Boresight error (angular pointing error) is then computed given the system effective focal length.
Using this information, STAR computes the complex system line-of-sight error (amplitude and phase) across all frequencies and determines LOS FRF which indicates the optical system sensitivity. The LOS FRF is then squared in magnitude and multiplied by the input PSD to obtain the LOS output PSD, following standard linear random vibration propagation:
PSDLOS(𝑓) = ∣FRFLOS(𝑓)∣2 PSDinput(𝑓)
Transverse image motion caused by dynamic structural excitation results in smearing of the image intensity across the detector plane. To quantify this degradation, we need to determine the jitter-induced modulation transfer function (MTF). For random image motion, the degradation in MTF is directly related to the root-mean-square (RMS) image displacement, allowing the optical performance impact to be expressed as a function of the RMS LOS motion. STAR Jitter module computes the RMS of the LOS response values by integrating the response PSD over the frequency range of interest and taking the square root of the enclosed area, and then finds the jitter MTF (Note: STAR Jitter module uses the weighted PSD as described in the next section.). The overall system MTF in the presence of jitter is then obtained by multiplying the nominal optical system MTF by the jitter MTF enabling direct assessment of image quality degradation due to reaction-wheel-induced disturbances.
MTFsystem = MTFnominal * MTFJitter
STAR Jitter module generates a report including input data and results as an HTML file. The LOS FRF, Response PSD for our CubeSat example under disturbance torque of a reaction wheel with a nominal speed of 6000 rpm are as follows (see the jitter report in the attachment). The PSD response curve helps identify the structural modes that contribute to the LOS error. According to the LOS PSD plot, the second harmonics is critical which is what we expected to see as it aligns with the first system natural frequency (first structural mode).
3- Integration-Time Filtering of LOS Disturbances
Sensor integration time does not alter the structural vibration or mechanical line-of-sight (LOS) motion itself, but it directly influences how that motion appears on the detector. In other words, integration time acts as a temporal filter on line-of-sight (LOS) motion. During the integration (exposure) period, the detector accumulates energy while the image may be moving due to dynamic disturbances. Integration time acts as a temporal averaging process, similar to adjusting the shutter speed of a camera to reduce motion blur.
The impact of integration time depends on the relationship between disturbance frequency and exposure duration. For high-frequency motion, many vibration cycles occur within a single integration period, causing the motion to oscillate about its mean position with little average pointing bias. In contrast, for low-frequency motion, only a fraction of a vibration cycle may occur during exposure, leading to image smear and an average pointing offset. For random vibration environments containing a range of frequencies, this effect is incorporated by applying frequency-dependent weighting functions to the LOS PSD as follows:
PSDLOS-eff(f) = W(f,Tint) ⋅ PSDLOS(f)
where W is the jitter weighting function defined as: W(f,Tint) = 1 – 2[1 – cos(C)] / C2
and C = 2πfTint, f is the frequency in Hz, and Tint is the sensor integration time.
The weighted PSD is then integrated to compute the effective RMS jitter, which is used to determine the corresponding degradation in modulation transfer function (MTF).
RMS jitter = ∫ PSDLOS-eff(f) df
The optical system MTF of the CubeSat for sensor integration time of 2ms and 5ms in the presence of optical jitter are compared with the nominal MTF in the graph below:
Discussion and Conclusion:
This work presented an integrated structural–optical workflow for predicting reaction-wheel-induced optical jitter in CubeSat systems by coupling frequency response analysis in ANSYS Mechanical with optical sensitivity modeling in STAR and Zemax. By propagating disturbance PSDs through structural FRFs to compute LOS motion, RMS jitter, and jitter-induced MTF degradation, while accounting for detector integration time, the methodology provides a practical and physics-based framework for quantifying and mitigating optical performance loss early in the CubeSat design process.
While structural dynamics determine the magnitude of line-of-sight (LOS) motion, the detector pixel size governs how that motion translates into image degradation. The RMS LOS jitter obtained from the structural–optical analysis is first converted to linear image-plane displacement using the system effective focal length. This yields the RMS image motion at the detector plane. By normalizing this displacement with the detector pixel pitch, the jitter can be expressed in units of pixels RMS, providing a direct measure of blur relative to the sensor sampling scale.
Pixel size directly influences the system’s sensitivity to jitter through its relationship with spatial sampling and Nyquist frequency. Smaller pixels increase the Nyquist frequency and therefore make the system more sensitive to high-spatial-frequency MTF degradation caused by image motion. Conversely, larger pixels reduce sampling frequency and may tolerate a given angular jitter more readily, although at the expense of spatial resolution. In the jitter MTF computation, the RMS image motion relative to pixel pitch determines the degree of attenuation at spatial frequencies near Nyquist. Expressing jitter in pixels RMS therefore provides a practical metric for evaluating whether the system is optics-limited, sampling-limited, or jitter-limited.
Acknowledgments:
The authors acknowledge Salmon Kalkhoran for his valuable assistance in polishing the structural model and enabling the export of STAR data from ANSYS Mechanical.
Additional Resources:
References:
Keith B. Doyle, Victor L. Genberg, Gregory J. Michels, Integrated Optomechanical Analysis, Second Edition, 2012, https://doi.org/10.1117/3.974624.ch7