There are some very old references (but in German):
The best function described is the one from Rodbard:
D. Rodbard, D.M. Hutt, Statistical Analysis of Radioimmunoassays and Immunoradiometric labeled antibody Assays: A Generalized Weighted, Iterative, Least-Squares Method for Logistic Curve Fitting. Radioimmunoassay and Related Procedures in Medicine 1, Vienna: Int. Atomic Energy Agency (1974) 165–192.
Kießig, ST, Gregor, P, Bellach, I, Porstmann, T, v.Baehr, R (1985) Entwicklung eines Programms für die rechnergestützte Auswertung von Enzymimmunoassays. Z med LabDiagn 26(6):347-349
Kießig, ST, Abel, U, Risse, P, Friedrich, J, Heinz, FX, Kunz, C (1993) Bestimmung von Schwellenwerten (Cut-Off) bei Enzymimmunoassays am Beispiel des FSME-ELISA. Klin Lab 39:877-886
Kießig, ST, Porstmann, T, Partowinia-Peters, M (1994) Auswertung von Enzymimmunoassays. GIT LabMed 17:58-64
all photometers have today a curve fitting included, the differences between a 3-, 4, or 5-parameter model is marginal.