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Pinging an old thread here. AC output SSRs are available with zero-cross and non-zero-cross outputs. The one shown in the images above, the SSR-25 DA, appears to be a non-zero-cross type that has the ability to provide less than full half-wave power to the load. This is done by turning detecting the zero-crossing of the input power and turning the SSR on after a precise delay. Of course driving an inductive load, particularly with a steel core, can make the relationship between the turn-on delay and power delivered to the load. Some SSR are specifically rated to handle inductive loads (SSRs not rated for inductive loads can fail to self-commutate meaning they might turn on and never turn off because they begin self triggering).
Girino - Fast Arduino Oscilloscope