The component orthogonal to the BL plane is given by applying Eq. (4) to the absorbance change $ak=(\Delta Ak,\lambda 1\Delta Ak,\lambda 2\Delta Ak,\lambda 3)T$. Because the first term of Eq. (12) is the absorbance change induced by the hemoglobin concentration change, the orthogonal component of this term is apparently zero. Thus, if the optical transmittance at a contact is independent of wavelength, the orthogonal component is given as Display Formula
$hk(t)=\u2212c1\u2009logr\u02dci(t)r\u02dcj(t)ri(0)rj(0)\u2212c2(t)r\u02dci(t)r\u02dcj(t)ri,0rj,0$(13)
Display Formula$=hmotion,k(t)+hnoise,k(t),$(14)
where Display Formula$hk(t)=uTak$(15)
Display Formula$c1=uT1$(16)
Display Formula$c2(t)=uT(nj,\lambda 1(t)/[Ii,\lambda 1Rk,\lambda 1(t)]nj,\lambda 2(t)/[Ii,\lambda 2Rk,\lambda 2(t)]nj,\lambda 3(t)/[Ii,\lambda 3Rk,\lambda 3(t)]),$(17)
and $1$ is a column vector whose elements are all 1. The first term in Eq. (14) corresponds to the body motion and contact instability, and the second term corresponds to the instrumental noise and contact weakness.