Figures 1a, 1b illustrate that the standard tone curve, a simple gamma 2.2 function or a BT.709 tone curve do not match actual output from a digital camera. Nor is it expected, see references.
Garcia JE, Dyer AG, Greentree AD, Spring G, Wilksch PA (2013) Linearisation of RGB Camera Responses for Quantitative Image Analysis of Visible and UV Photography: A Comparison of Two Techniques. PLoS ONE 8(11): e79534. doi:10.1371/journal.pone.0079534
"camera responses... successfully fitted the entire characteristic curve of the tested devices, allowing for an accurate recovery of linear camera responses."
"Linear responses from consumer-level cameras can be recov- ered by fitting a function to a plot of camera response versus incident radiance, the Opto-Electronic Conversion Function curve (OECF), and subsequently inverting the fitting function via analytical or graphical methods, or look-up tables (LUTs) . Polynomial, power and exponential functions have been previ- ously suggested as fitting functions [20,21]."
"Here we compare the use of (parametric) cubic Be ́zier curves and biexponential functions for characterising two camera models"
"In spite of being sensitive to different regions of the spectrum, the OECF curves of the two tested cameras present a notable similarity in their general form. This result indicates a close likeness between the gain functions applied to the sensor response of the two cameras."
Assuming an sRGB response curve (as described in Chapter 2) is unwise, because most makers boost image contrast beyond the standard sRGB gamma to produce a livelier image. There is often some modification as well at the ends of the curves, to provide softer highlights and reduce noise visibility in shadows.
http://www.ee.columbia.edu/ln/dvmm/publications/PhD_theses/jessiehsu_thesis.pdf Image Tampering Detection For Forensics Applications PhD These, Columbia U, 2009
"Camera Response Function (CRF), pages 37-38: The CRF is often denoted as a single-variable function R=f(r). Although diffㄦent manufacturers may produce diffㄦent dynamic ranges of irradiance r and brightness R, without loss of generality, both r and R are assumed to be between [0,1]. Some popular parameterized models are listed as follows:"
PCA-based empirical model of response (EMOR) 
Single-parameter gamma function R=f(r) = r^a0 
Polynomial R = f(r) = SUM n=0 to N r^Bn [33
Generalized gamma curve model (GGCM) R =f(r) =r SUM i=0 to n ai *r6^i [34, 35]
"Generally, more parameters lead to more accurate representations of the CRF with the drawback of increased complexity. Therefore one should choose an optimal model considering the tradeoâetween approximation accuracy and computational complexity. A comparison among these models is given in  and . The EMOR and GGCM have been shown to approximate CRFs better than the gamma and polynomial models."
the above reference 31 is:
 M. D. Grossberg and S. K. Nayar. What is the space of camera response functions? IEEE Conference on Computer Vision and Pattern Recognition, 2003.
"a camera's response function can vary significantly from an analytic form like a gamma curve."
Last updated June 28, 2015