Value chain · CLM-0913
In plain terms
When the satellite corrects its own bending by listening to the ground signal, what is left over is not how far the antennas moved. It is only the part of that movement the scattered sensors could not see. A structure that bows a metre smoothly, with sensors close enough to follow the bow, is barely affected; a millimetre of movement between sensors costs the full millimetre. If the frequency scaling is exact, the frequency of the ground signal drops out of the answer.
The claim as recorded
For retrodirective phase conjugation with phase sampled at dispersed detectors and interpolated to the elements between them, the residual phase error at element n is eps_n = k_t ( s_n - I_n[s] ) + O(d^2/L), where k_t is the TRANSMIT wavenumber, s_n is the LINE-OF-SIGHT component of element n's displacement, and I_n is the interpolation operator. Under exact frequency scaling the pilot wavenumber cancels exactly, so the pilot's wavelength does not set the position tolerance and the transmit wavelength does - and heterodyne hardware does not scale exactly, which is CLM-0914: there the pilot frequency re-enters through dk. The sensitivity is therefore not to displacement but to the part of the line-of-sight displacement field the interpolation cannot represent. The neglected term is O(d^2/L): at metre-scale displacement and geostationary range it is about 2.8e-8 m, five orders of magnitude below the 2.955 mm position tolerance of CLM-0901, and it falls as the square of the displacement.
Evidence behind this: T0-derivation. Closed-form result derived here from the disclosed architecture. This record's support carries the eps_n derivation and the d^2/L check; CALC-106 holds equation (7) only.
Scope and limits
First order in displacement. Exact in the sense that the cancellation of the true position in the focusing law is exact, not first-order; the linearisation is only in the step from range error to line-of-sight displacement. Static. Every term here is instantaneous. A real loop samples at intervals while the structure moves between samples, and that adds a term this result does not contain. Detector measurement noise is not modelled and does not interpolate away - it worsens with fewer detectors, pushing opposite to CLM-0912. No structural model is held - see CLM-0907 - so nothing here converts to a spacing in metres.
What it assumes
That the interpolation operator is constructed to be exact on the design geometry. That the frequency scaling of the measured phase is applied correctly - the condition under which that is possible at all is CLM-0914, registered 2026-09-14, which establishes that a frequency offset reduces the displacement error by f_t/df rather than removing it.
Where it comes from
This is the project's own working, shown in full:
CALC-106. Derivation: the pilot from target R reaches element n with phase k_p L(r_n); conjugating and scaling by k_t/k_p gives exactly the focusing law phi_n = -k_t L(r_n) + const, in which the true position does not appear. Interpolating instead of measuring leaves eps_n = k_t ( L(r_n) - I_n[L(p_j)] ), and expanding about the design geometry, on which the interpolation operator is exact by construction, gives the stated first-order form. NEGLECTED TERM RECOMPUTED ON REGISTRATION, 2026-09-14. d^2/L at d = 1 m and L = 35,786 km is 2.794e-8 m, or 1.397e-8 m for d^2/2L; against the 2.955 mm tolerance that is a factor of 9.5e-6. At d = 1 mm the term is 2.794e-14 m.
Basis: radians (phase residual); metres (line-of-sight displacement)
Related records
- Answers question
- QST-013 not published in this release
Cite this
energyaperture.com/c/clm-0913
CLM-0913, Energy Aperture, as of 2026-09-13.
Connected records
Other published records linked to this one. A list, not a judgement.
- Also from SRC-088
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