Summary:
In response to the recent CW injection recovery report, I investigated why there is a ~61 usec delay residual (see this plot, as well as the attached plot with 61 usec delay plotted), and to understand the amplitude offset (see this plot). I have identified that there was a missing 61 usec delay that should have been included in the inverse actuation filtering assumed timing advance, see below. The transfer function provided to the CW group for hardware injections is similarly affected, and requires including a 61 usec advance. This resolves the phase offset issue as seen in the CW injections. Amplitude offsets are a little more complicated without comparing with the true injected waveform; see below.

Details:
First, addressing the amplitude offset: the calibration team carefully monitors the photon calibrator power sent to the test mass using a calibrated photodetector sampling a fraction of the beam sent to the ETM, or reading back the full beam reflected from the test mass. This ensures we know exactly how much the mass was actually displaced by the radiation pressure. The inverse actuation filter used by hardware injections relies on a calibrated excitation point, which is less reliable than the readback photodetectors. Thus, I would not rely on this calibration to better than the ~5 percent level. Also, the inverse actuation filter has a gain on the anti-(analog AI) of 1.0098. This is because there have been measurements at LHO to show that at least some of the analog AI chassis have a gain of 1/1.0098 = 0.9903 (see LHO aLOGs 18628 and 18518), whereas LLO sets the model to have unity gain and allow for an offset (see LLO aLOG 18315). So there is some uncertainty on the overall gain of the inverse actuation filter at the ~1% level due to the AI gain alone. Thus, for better comparison of the CW hardware injection amplitudes, it would be better to analyze the photodiode readback channels to verify the expected waveform matches what was actually injected.

For the residual phase, the originally quoted uncompensated delay was ~240 usec (see LLO aLOG 27562). The delay is a combination of the digital delays, as well as any residual phase effects from the approximated AI filtering and roll-off filters which would require time advances (not possible in Foton). Well, it turns out that I neglected to include the 61 usec delay when summing the digital delays. (D'oh!) Thus, the uncompensated delay is not ~240 usec but rather ~300 usec.

The hardware injection pathway from a given waveform, through the inverse actuation filter, through the Pcal output generating strain, can be expressed as: 

          m     N             1        W     V      1      cts      1                                                              V              W     N                 1      m     h
h(t) x [ --- x --- x f^2 x -------- x --- x --- x ----- x ----- x ----- x roll-off ] x [ 61 usec delay x AI(D) x 61 usec delay x ----- x AI(a) x --- x --- x sus.norm x ----- x --- x --- ]
          h     m          sus.norm    N     W    AI(a)     V     AI(D)                                                           cts             V     W                f^2     N     m

where the first term in brackets is the inverse actuation filter (not accounting for any digital delays) and the second term in brackets are the pieces lying between the Pcal excitation point and the induced strain. I had neglected to include the first 61 usec delay in the second bracketed term. It can be easier to see the accounting of delays in this DCC diagram and Pcal path components in the calibration subway map.

Fortunately, this resolves the issue with CW injections, since they will have a 61 usec delay induced due to this oversight. It also means that all other injections should assume a ~300 usec timing advance in all waveforms.

I also attach an updated file to be used for H1 CW hardware injections that includes the missing 61 usec advance to account for the 61 usec delay.