Revenue - Business Revenue (Details) - USD ($) $ in Millions	3 Months Ended
	Dec. 28, 2019	Dec. 29, 2018
Disaggregation of Revenue [Line Items]
Revenues	$ 850.5	$ 830.7
United States
Disaggregation of Revenue [Line Items]
Revenues	632.7	621.8
International
Disaggregation of Revenue [Line Items]
Revenues	217.8	208.9
Diagnostics
Disaggregation of Revenue [Line Items]
Revenues	311.5	296.6
Diagnostics | United States
Disaggregation of Revenue [Line Items]
Revenues	231.6	227.5
Diagnostics | International
Disaggregation of Revenue [Line Items]
Revenues	79.9	69.1
Diagnostics | Cytology & Perinatal
Disaggregation of Revenue [Line Items]
Revenues	121.0	118.1
Diagnostics | Cytology & Perinatal | United States
Disaggregation of Revenue [Line Items]
Revenues	77.5	79.2
Diagnostics | Cytology & Perinatal | International
Disaggregation of Revenue [Line Items]
Revenues	43.5	38.9
Diagnostics | Molecular Diagnostics
Disaggregation of Revenue [Line Items]
Revenues	178.5	164.3
Diagnostics | Molecular Diagnostics | United States
Disaggregation of Revenue [Line Items]
Revenues	142.1	134.1
Diagnostics | Molecular Diagnostics | International
Disaggregation of Revenue [Line Items]
Revenues	36.4	30.2
Diagnostics | Blood Screening
Disaggregation of Revenue [Line Items]
Revenues	12.0	14.2
Diagnostics | Blood Screening | United States
Disaggregation of Revenue [Line Items]
Revenues	12.0	14.2
Diagnostics | Blood Screening | International
Disaggregation of Revenue [Line Items]
Revenues	0.0	0.0
Breast Health
Disaggregation of Revenue [Line Items]
Revenues	331.1	324.7
Breast Health | United States
Disaggregation of Revenue [Line Items]
Revenues	256.5	252.6
Breast Health | International
Disaggregation of Revenue [Line Items]
Revenues	74.6	72.1
Breast Health | Breast Imaging
Disaggregation of Revenue [Line Items]
Revenues	274.8	269.7
Breast Health | Breast Imaging | United States
Disaggregation of Revenue [Line Items]
Revenues	209.4	206.5
Breast Health | Breast Imaging | International
Disaggregation of Revenue [Line Items]
Revenues	65.4	63.2
Breast Health | Interventional Breast Solutions
Disaggregation of Revenue [Line Items]
Revenues	56.3	55.0
Breast Health | Interventional Breast Solutions | United States
Disaggregation of Revenue [Line Items]
Revenues	47.1	46.1
Breast Health | Interventional Breast Solutions | International
Disaggregation of Revenue [Line Items]
Revenues	9.2	8.9
GYN Surgical
Disaggregation of Revenue [Line Items]
Revenues	119.1	108.4
GYN Surgical | United States
Disaggregation of Revenue [Line Items]
Revenues	98.8	91.1
GYN Surgical | International
Disaggregation of Revenue [Line Items]
Revenues	20.3	17.3
Medical Aesthetics
Disaggregation of Revenue [Line Items]
Revenues	65.3	79.8
Medical Aesthetics | United States
Disaggregation of Revenue [Line Items]
Revenues	30.9	37.3
Medical Aesthetics | International
Disaggregation of Revenue [Line Items]
Revenues	34.4	42.5
Skeletal Health
Disaggregation of Revenue [Line Items]
Revenues	23.5	21.2
Skeletal Health | United States
Disaggregation of Revenue [Line Items]
Revenues	14.9	13.3
Skeletal Health | International
Disaggregation of Revenue [Line Items]
Revenues	$ 8.6	$ 7.9